diff --git a/src/sage/algebras/quatalg/quaternion_algebra_cython.pyx b/src/sage/algebras/quatalg/quaternion_algebra_cython.pyx
index 983e2515c04..130c9f5d43a 100644
--- a/src/sage/algebras/quatalg/quaternion_algebra_cython.pyx
+++ b/src/sage/algebras/quatalg/quaternion_algebra_cython.pyx
@@ -35,7 +35,7 @@ from sage.matrix.matrix_space import MatrixSpace
 from sage.matrix.matrix_integer_dense cimport Matrix_integer_dense
 from sage.matrix.matrix_rational_dense cimport Matrix_rational_dense
 
-from .quaternion_algebra_element cimport QuaternionAlgebraElement_rational_field
+from sage.algebras.quatalg.quaternion_algebra_element cimport QuaternionAlgebraElement_rational_field
 
 from sage.libs.gmp.mpz cimport mpz_t, mpz_lcm, mpz_init, mpz_set, mpz_clear, mpz_init_set, mpz_mul, mpz_fdiv_q, mpz_cmp_si
 
diff --git a/src/sage/categories/action.pyx b/src/sage/categories/action.pyx
index b164e9213ce..0e54ceffa27 100644
--- a/src/sage/categories/action.pyx
+++ b/src/sage/categories/action.pyx
@@ -91,7 +91,7 @@ cdef class Action(Functor):
       :class:`Action` itself, but other classes may use it
     """
     def __init__(self, G, S, is_left=True, op=None):
-        from .groupoid import Groupoid
+        from sage.categories.groupoid import Groupoid
         Functor.__init__(self, Groupoid(G), category(S))
         self.G = G
         self.US = ref(S)
diff --git a/src/sage/categories/morphism.pyx b/src/sage/categories/morphism.pyx
index 32fcd565e34..a30cf52e5c9 100644
--- a/src/sage/categories/morphism.pyx
+++ b/src/sage/categories/morphism.pyx
@@ -467,7 +467,7 @@ cdef class CallMorphism(Morphism):
 cdef class IdentityMorphism(Morphism):
 
     def __init__(self, parent):
-        from .homset import Homset, Hom
+        from sage.categories.homset import Homset, Hom
         if not isinstance(parent, Homset):
             parent = Hom(parent, parent)
         Morphism.__init__(self, parent)
diff --git a/src/sage/cpython/getattr.pyx b/src/sage/cpython/getattr.pyx
index 3a06167ea99..e4982020879 100644
--- a/src/sage/cpython/getattr.pyx
+++ b/src/sage/cpython/getattr.pyx
@@ -4,7 +4,7 @@ Variants of getattr()
 
 from cpython.object cimport PyObject, PyTypeObject, Py_TYPE, descrgetfunc
 
-from .string cimport bytes_to_str
+from sage.cpython.string cimport bytes_to_str
 
 cdef extern from "Python.h":
     r"""
diff --git a/src/sage/cpython/wrapperdescr.pyx b/src/sage/cpython/wrapperdescr.pyx
index 108ca690b8d..5738a87af46 100644
--- a/src/sage/cpython/wrapperdescr.pyx
+++ b/src/sage/cpython/wrapperdescr.pyx
@@ -30,7 +30,7 @@ Pure Python classes have normal methods, not slot wrappers::
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from .string import bytes_to_str
+from sage.cpython.string import bytes_to_str
 
 
 def wrapperdescr_call(slotwrapper, self, *args, **kwds):
diff --git a/src/sage/misc/cachefunc.pxd b/src/sage/misc/cachefunc.pxd
index 747e9b60df0..5590c41f4d3 100644
--- a/src/sage/misc/cachefunc.pxd
+++ b/src/sage/misc/cachefunc.pxd
@@ -1,4 +1,4 @@
-from .function_mangling cimport ArgumentFixer
+from sage.misc.function_mangling cimport ArgumentFixer
 
 cpdef dict_key(o) noexcept
 cpdef cache_key(o) noexcept
diff --git a/src/sage/misc/lazy_import.pyx b/src/sage/misc/lazy_import.pyx
index 0ac9fb03d95..c9b09dc1ef5 100644
--- a/src/sage/misc/lazy_import.pyx
+++ b/src/sage/misc/lazy_import.pyx
@@ -66,7 +66,7 @@ import os
 import pickle
 from warnings import warn
 import inspect
-from . import sageinspect
+from sage.misc import sageinspect
 
 
 # LazyImport.__repr__ uses try... except FeatureNotPresentError.
@@ -1137,7 +1137,7 @@ def save_cache_file():
         sage: sage.misc.lazy_import.save_cache_file()
     """
     from sage.misc.temporary_file import atomic_write
-    from .lazy_import_cache import get_cache_file
+    from sage.misc.lazy_import_cache import get_cache_file
 
     global star_imports
     if star_imports is None:
@@ -1180,7 +1180,7 @@ def get_star_imports(module_name):
     """
     global star_imports
     if star_imports is None:
-        from .lazy_import_cache import get_cache_file
+        from sage.misc.lazy_import_cache import get_cache_file
         star_imports = {}
         try:
             with open(get_cache_file(), "rb") as cache_file:
diff --git a/src/sage/misc/persist.pyx b/src/sage/misc/persist.pyx
index 670a9a6ac17..5bbc32a239a 100644
--- a/src/sage/misc/persist.pyx
+++ b/src/sage/misc/persist.pyx
@@ -42,7 +42,7 @@ import bz2
 comp = zlib
 comp_other = bz2
 
-from .sage_unittest import TestSuite
+from sage.misc.sage_unittest import TestSuite
 
 
 # We define two global dictionaries `already_pickled` and
@@ -1237,7 +1237,7 @@ def db(name):
 
     The database directory is ``$HOME/.sage/db``.
     """
-    from .misc import SAGE_DB
+    from sage.misc.misc import SAGE_DB
     return load('%s/%s'%(SAGE_DB,name))
 
 
@@ -1250,5 +1250,5 @@ def db_save(x, name=None):
     try:
         x.db(name)
     except AttributeError:
-        from .misc import SAGE_DB
+        from sage.misc.misc import SAGE_DB
         save(x, '%s/%s'%(SAGE_DB,name))
diff --git a/src/sage/misc/sage_timeit_class.pyx b/src/sage/misc/sage_timeit_class.pyx
index 5537148e358..f568886574f 100644
--- a/src/sage/misc/sage_timeit_class.pyx
+++ b/src/sage/misc/sage_timeit_class.pyx
@@ -6,7 +6,7 @@ The ``timeit`` command
 This uses the function :func:`~sage.misc.sage_timeit.sage_timeit`.
 """
 
-from . import sage_timeit
+from sage.misc import sage_timeit
 
 
 class SageTimeit:
diff --git a/src/sage/modular/modsym/heilbronn.pyx b/src/sage/modular/modsym/heilbronn.pyx
index ba42d70aa9e..7fc8ed28055 100644
--- a/src/sage/modular/modsym/heilbronn.pyx
+++ b/src/sage/modular/modsym/heilbronn.pyx
@@ -34,11 +34,11 @@ cdef extern from "<math.h>":
     float roundf(float x)
 
 cimport sage.modular.modsym.p1list as p1list
-from . import p1list
+from sage.modular.modsym import p1list
 cdef p1list.export export
 export = p1list.export()
 
-from .apply cimport Apply
+from sage.modular.modsym.apply cimport Apply
 cdef Apply PolyApply= Apply()
 
 from sage.matrix.matrix_rational_dense cimport Matrix_rational_dense
diff --git a/src/sage/modular/pollack_stevens/dist.pyx b/src/sage/modular/pollack_stevens/dist.pyx
index fe1f5583cd5..3f67bbf8ecb 100644
--- a/src/sage/modular/pollack_stevens/dist.pyx
+++ b/src/sage/modular/pollack_stevens/dist.pyx
@@ -44,7 +44,7 @@ from sage.rings.infinity import Infinity
 
 #from sage.libs.flint.ulong_extras cimport *
 
-from .sigma0 import Sigma0
+from sage.modular.pollack_stevens.sigma0 import Sigma0
 
 cdef long overflow = 1 << (4 * sizeof(long) - 1)
 cdef long underflow = -overflow
diff --git a/src/sage/rings/complex_double.pyx b/src/sage/rings/complex_double.pyx
index 944bcc5aa27..f101960aab8 100644
--- a/src/sage/rings/complex_double.pyx
+++ b/src/sage/rings/complex_double.pyx
@@ -213,7 +213,7 @@ cdef class ComplexDoubleField_class(sage.rings.abc.ComplexDoubleField):
             sage: CDF.characteristic()
             0
         """
-        from .integer import Integer
+        from sage.rings.integer import Integer
         return Integer(0)
 
     def random_element(self, double xmin=-1, double xmax=1, double ymin=-1, double ymax=1):
@@ -351,7 +351,7 @@ cdef class ComplexDoubleField_class(sage.rings.abc.ComplexDoubleField):
             sage: CDF((1,2)) # indirect doctest
             1.0 + 2.0*I
         """
-        from . import complex_mpfr
+        from sage.rings import complex_mpfr
         if isinstance(x, ComplexDoubleElement):
             return x
         elif isinstance(x, tuple):
@@ -417,10 +417,10 @@ cdef class ComplexDoubleField_class(sage.rings.abc.ComplexDoubleField):
         """
         if S is int or S is float:
             return FloatToCDF(S)
-        from .rational_field import QQ
-        from .real_lazy import RLF
-        from .real_mpfr import RR
-        from .cc import CC
+        from sage.rings.rational_field import QQ
+        from sage.rings.real_lazy import RLF
+        from sage.rings.real_mpfr import RR
+        from sage.rings.cc import CC
 
         if S is ZZ or S is QQ or S is RDF or S is RLF:
             return FloatToCDF(S)
@@ -502,7 +502,7 @@ cdef class ComplexDoubleField_class(sage.rings.abc.ComplexDoubleField):
         if prec == 53:
             return self
         else:
-            from .complex_mpfr import ComplexField
+            from sage.rings.complex_mpfr import ComplexField
             return ComplexField(prec)
 
 
@@ -621,7 +621,7 @@ cdef class ComplexDoubleField_class(sage.rings.abc.ComplexDoubleField):
             ...
             ValueError: n must be a positive integer
         """
-        from .integer import Integer
+        from sage.rings.integer import Integer
         try:
             n = Integer(n)
         except TypeError:
@@ -968,7 +968,7 @@ cdef class ComplexDoubleElement(FieldElement):
             True
         """
         # Sending to another computer algebra system is slow anyway, right?
-        from .complex_mpfr import ComplexField
+        from sage.rings.complex_mpfr import ComplexField
         return ComplexField()(self)._interface_init_(I)
 
     def _mathematica_init_(self):
@@ -980,7 +980,7 @@ cdef class ComplexDoubleElement(FieldElement):
             sage: mathematica(CDF(1e-25, 1e25))  # optional - mathematica
             1.*^-25 + 1.*^25*I
         """
-        from .complex_mpfr import ComplexField
+        from sage.rings.complex_mpfr import ComplexField
         return ComplexField()(self)._mathematica_init_()
 
     def _maxima_init_(self, I=None):
@@ -995,7 +995,7 @@ cdef class ComplexDoubleElement(FieldElement):
             sage: CDF(.5 + I)._maxima_init_()                                           # needs sage.symbolic
             '0.50000000000000000 + 1.0000000000000000*%i'
         """
-        from .complex_mpfr import ComplexField
+        from sage.rings.complex_mpfr import ComplexField
         return ComplexField()(self)._maxima_init_(I)
 
     def _sympy_(self):
@@ -1097,7 +1097,7 @@ cdef class ComplexDoubleElement(FieldElement):
             sage: format(CDF(0, 0), '+#.4')
             '+0.000'
         """
-        from .complex_mpfr import _format_complex_number
+        from sage.rings.complex_mpfr import _format_complex_number
         return _format_complex_number(GSL_REAL(self._complex),
                                                      GSL_IMAG(self._complex),
                                                      format_spec)
@@ -2382,12 +2382,12 @@ cdef class ComplexDoubleElement(FieldElement):
         """
         if not GSL_IMAG(self._complex):
             if GSL_REAL(self._complex) == 0:
-                from .infinity import unsigned_infinity
+                from sage.rings.infinity import unsigned_infinity
                 return unsigned_infinity
             try:
-                from .integer import Integer
+                from sage.rings.integer import Integer
                 if Integer(GSL_REAL(self._complex)) < 0:
-                    from .cc import CC
+                    from sage.rings.cc import CC
                     return CC(self).gamma()
             except TypeError:
                 pass
@@ -2429,7 +2429,7 @@ cdef class ComplexDoubleElement(FieldElement):
             Infinity
         """
         if GSL_REAL(self._complex) == 1 and GSL_IMAG(self._complex) == 0:
-            from .infinity import unsigned_infinity
+            from sage.rings.infinity import unsigned_infinity
             return unsigned_infinity
 
         global complex_double_element_zeta
diff --git a/src/sage/rings/complex_interval.pyx b/src/sage/rings/complex_interval.pyx
index 5b7a04fef10..e804964f501 100644
--- a/src/sage/rings/complex_interval.pyx
+++ b/src/sage/rings/complex_interval.pyx
@@ -1914,7 +1914,7 @@ cdef class ComplexIntervalFieldElement(FieldElement):
             0.500000000000000? + 3.39927010637040?*I
         """
         if not self:
-            from .real_mpfi import RIF
+            from sage.rings.real_mpfi import RIF
             return RIF(0).log()
         re = abs(self).log()
         im = self.argument()
@@ -2291,6 +2291,6 @@ def create_ComplexIntervalFieldElement(s_real, s_imag=None, int pad=0, min_prec=
     #else:
     #    bits = max(int(math.log(base,2)*len(s_imag)),int(math.log(base,2)*len(s_imag)))
 
-    from .complex_interval_field import ComplexIntervalField
+    from sage.rings.complex_interval_field import ComplexIntervalField
     C = ComplexIntervalField(prec=max(bits+pad, min_prec))
     return ComplexIntervalFieldElement(C, s_real, s_imag)
diff --git a/src/sage/rings/complex_mpc.pyx b/src/sage/rings/complex_mpc.pyx
index 7a9ab37e268..6f727bb4c59 100644
--- a/src/sage/rings/complex_mpc.pyx
+++ b/src/sage/rings/complex_mpc.pyx
@@ -105,8 +105,8 @@ def late_import():
         import sage.rings.qqbar
         AA = sage.rings.qqbar.AA
         QQbar = sage.rings.qqbar.QQbar
-        from .real_lazy import CLF, RLF
-        from .complex_double import CDF
+        from sage.rings.real_lazy import CLF, RLF
+        from sage.rings.complex_double import CDF
 
 _mpfr_rounding_modes = ['RNDN', 'RNDZ', 'RNDU', 'RNDD']
 
diff --git a/src/sage/rings/complex_mpfr.pyx b/src/sage/rings/complex_mpfr.pyx
index 6e2412afac7..3b0ff5c0c1d 100644
--- a/src/sage/rings/complex_mpfr.pyx
+++ b/src/sage/rings/complex_mpfr.pyx
@@ -102,8 +102,8 @@ def late_import():
         QQbar = sage.rings.qqbar.QQbar
         import sage.symbolic.ring
         SR = sage.symbolic.ring.SR
-        from .real_lazy import CLF, RLF
-        from .complex_double import CDF
+        from sage.rings.real_lazy import CLF, RLF
+        from sage.rings.complex_double import CDF
 
 cdef object numpy_complex_interface = {'typestr': '=c16'}
 cdef object numpy_object_interface = {'typestr': '|O'}
@@ -372,7 +372,7 @@ class ComplexField_class(sage.rings.abc.ComplexField):
         try:
             return self.__real_field
         except AttributeError:
-            from .real_mpfr import RealField
+            from sage.rings.real_mpfr import RealField
             self.__real_field = RealField(self._prec)
             return self.__real_field
 
@@ -2931,7 +2931,7 @@ cdef class ComplexNumber(sage.structure.element.FieldElement):
         if base is None:
             return ComplexNumber(self._parent, rho.log(), theta)
         else:
-            from .real_mpfr import RealField
+            from sage.rings.real_mpfr import RealField
             return ComplexNumber(self._parent, rho.log()/RealNumber(RealField(self.prec()),base).log(), theta/RealNumber(RealField(self.prec()),base).log())
 
     def additive_order(self):
diff --git a/src/sage/rings/finite_rings/finite_field_base.pyx b/src/sage/rings/finite_rings/finite_field_base.pyx
index cc2d1b65dd0..dd79b0d90b9 100644
--- a/src/sage/rings/finite_rings/finite_field_base.pyx
+++ b/src/sage/rings/finite_rings/finite_field_base.pyx
@@ -1045,7 +1045,7 @@ cdef class FiniteField(Field):
             pass
 
         from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-        from .finite_field_constructor import GF
+        from sage.rings.finite_rings.finite_field_constructor import GF
         R = PolynomialRing(GF(self.characteristic()), 'x')
         self._modulus = R((-1,1))  # Polynomial x - 1
         return self._modulus
@@ -1288,7 +1288,7 @@ cdef class FiniteField(Field):
             inclusion_map = self.coerce_map_from(base)
 
         from sage.matrix.constructor import matrix
-        from .maps_finite_field import (
+        from sage.rings.finite_rings.maps_finite_field import (
             MorphismVectorSpaceToFiniteField, MorphismFiniteFieldToVectorSpace)
 
         E = self
@@ -1379,7 +1379,7 @@ cdef class FiniteField(Field):
         if isinstance(R, FiniteField):
             if R is self:
                 return True
-            from .residue_field import ResidueField_generic
+            from sage.rings.finite_rings.residue_field import ResidueField_generic
             if isinstance(R, ResidueField_generic):
                 return False
             if R.characteristic() == self.characteristic():
@@ -1543,7 +1543,7 @@ cdef class FiniteField(Field):
             sage: L(u).minpoly() == u.minpoly()
             True
         """
-        from .finite_field_constructor import GF
+        from sage.rings.finite_rings.finite_field_constructor import GF
         from sage.rings.polynomial.polynomial_element import Polynomial
         from sage.rings.integer import Integer
         if name is None and names is not None:
@@ -1719,7 +1719,7 @@ cdef class FiniteField(Field):
             sage: GF(3^8, 'a').subfield(4)
             Finite Field in a4 of size 3^4
         """
-        from .finite_field_constructor import GF
+        from sage.rings.finite_rings.finite_field_constructor import GF
         p = self.characteristic()
         n = self.degree()
         if not n % degree == 0:
@@ -1926,7 +1926,7 @@ cdef class FiniteField(Field):
             sage: GF(next_prime(2^16, 2), 'a').is_conway()
             False
         """
-        from .conway_polynomials import conway_polynomial, exists_conway_polynomial
+        from sage.rings.finite_rings.conway_polynomials import conway_polynomial, exists_conway_polynomial
         p = self.characteristic()
         n = self.degree()
         return (exists_conway_polynomial(p, n)
diff --git a/src/sage/rings/finite_rings/hom_finite_field.pyx b/src/sage/rings/finite_rings/hom_finite_field.pyx
index 5f54c04dd36..85dadd6fb2c 100644
--- a/src/sage/rings/finite_rings/hom_finite_field.pyx
+++ b/src/sage/rings/finite_rings/hom_finite_field.pyx
@@ -763,7 +763,7 @@ cdef class FrobeniusEndomorphism_finite_field(FrobeniusEndomorphism_generic):
         """
         if self._degree_fixed == 1:
             k = FiniteField(self.domain().characteristic())
-            from .hom_prime_finite_field import FiniteFieldHomomorphism_prime
+            from sage.rings.finite_rings.hom_prime_finite_field import FiniteFieldHomomorphism_prime
             f = FiniteFieldHomomorphism_prime(Hom(k, self.domain()))
         else:
             k = FiniteField(self.domain().characteristic()**self._degree_fixed,
diff --git a/src/sage/rings/finite_rings/integer_mod.pyx b/src/sage/rings/finite_rings/integer_mod.pyx
index d715cec1493..d687c4bf50c 100644
--- a/src/sage/rings/finite_rings/integer_mod.pyx
+++ b/src/sage/rings/finite_rings/integer_mod.pyx
@@ -153,7 +153,7 @@ def Mod(n, m, parent=None):
 
     # m is non-zero, so return n mod m
     if parent is None:
-        from .integer_mod_ring import IntegerModRing
+        from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
         parent = IntegerModRing(m)
     return IntegerMod(parent, n)
 
@@ -493,7 +493,7 @@ cdef class IntegerMod_abstract(FiniteRingElement):
         if not isinstance(self, IntegerMod_abstract):
             # something % Mod(x,y) makes no sense
             return NotImplemented
-        from .integer_mod_ring import IntegerModRing
+        from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
         R = IntegerModRing(modulus)
         if (<Element>self)._parent._IntegerModRing_generic__order % R.order():
             raise ArithmeticError(f"reduction modulo {modulus!r} not defined")
@@ -1227,7 +1227,7 @@ cdef class IntegerMod_abstract(FiniteRingElement):
                 R = self.parent()['x']
                 modulus = R.gen()**2 - R(self)
                 if self._parent.is_field():
-                    from .finite_field_constructor import FiniteField
+                    from sage.rings.finite_rings.finite_field_constructor import FiniteField
                     Q = FiniteField(self._modulus.sageInteger**2, y, modulus)
                 else:
                     R = self.parent()['x']
@@ -1437,7 +1437,7 @@ cdef class IntegerMod_abstract(FiniteRingElement):
             ....:         if (y^41).nth_root(41*r)**(41*r) != y^41: raise RuntimeError
             ....:         if (y^307).nth_root(307*r)**(307*r) != y^307: raise RuntimeError
 
-            sage: for t in range(200):                                                  # needs sage.libs.pari
+            sage: for t in range(200):                                                  # needs sage.libs.pari sage.rings.padics
             ....:     n = randint(1,2^63)
             ....:     K = Integers(n)
             ....:     b = K.random_element()
@@ -2137,7 +2137,7 @@ cdef class IntegerMod_gmp(IntegerMod_abstract):
 
         modulus = self._modulus.sageInteger
         other_modulus = other._modulus.sageInteger
-        from .integer_mod_ring import IntegerModRing
+        from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
         lift = IntegerMod_gmp(IntegerModRing(modulus*other_modulus))
         try:
             if mpz_cmp(self.value, other.value) > 0:
@@ -2541,7 +2541,7 @@ cdef class IntegerMod_int(IntegerMod_abstract):
         cdef IntegerMod_int lift
         cdef int_fast32_t x
 
-        from .integer_mod_ring import IntegerModRing
+        from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
         lift = IntegerMod_int(IntegerModRing(self._modulus.int32 * other._modulus.int32))
 
         try:
@@ -3377,7 +3377,7 @@ cdef class IntegerMod_int64(IntegerMod_abstract):
         cdef IntegerMod_int64 lift
         cdef int_fast64_t x
 
-        from .integer_mod_ring import IntegerModRing
+        from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
         lift = IntegerMod_int64(IntegerModRing(self._modulus.int64 * other._modulus.int64))
 
         try:
diff --git a/src/sage/rings/finite_rings/residue_field.pyx b/src/sage/rings/finite_rings/residue_field.pyx
index 9845266870a..e84b303769a 100644
--- a/src/sage/rings/finite_rings/residue_field.pyx
+++ b/src/sage/rings/finite_rings/residue_field.pyx
@@ -386,7 +386,7 @@ class ResidueFieldFactory(UniqueFactory):
                 q = characteristic**(f.degree())
                 if q < zech_log_bound and (impl is None or impl == 'givaro'):
                     try:
-                        from .residue_field_givaro import ResidueFiniteField_givaro
+                        from sage.rings.finite_rings.residue_field_givaro import ResidueFiniteField_givaro
                     except ImportError:
                         if impl is not None:
                             raise
@@ -394,7 +394,7 @@ class ResidueFieldFactory(UniqueFactory):
                         return ResidueFiniteField_givaro(p, q, names, f, None, None, None)
                 if q % 2 == 0 and (impl is None or impl == 'ntl'):
                     try:
-                        from .residue_field_ntl_gf2e import ResidueFiniteField_ntl_gf2e
+                        from sage.rings.finite_rings.residue_field_ntl_gf2e import ResidueFiniteField_ntl_gf2e
                     except ImportError:
                         if impl is not None:
                             raise
@@ -402,7 +402,7 @@ class ResidueFieldFactory(UniqueFactory):
                         return ResidueFiniteField_ntl_gf2e(q, names, f, "poly", p, None, None, None)
                 if impl is None or impl == 'pari':
                     try:
-                        from .residue_field_pari_ffelt import ResidueFiniteField_pari_ffelt
+                        from sage.rings.finite_rings.residue_field_pari_ffelt import ResidueFiniteField_pari_ffelt
                     except ImportError:
                         if impl is not None:
                             raise
@@ -462,7 +462,7 @@ class ResidueFieldFactory(UniqueFactory):
             q = characteristic**(f.degree())
             if q < zech_log_bound and (impl is None or impl == 'givaro'):
                 try:
-                    from .residue_field_givaro import ResidueFiniteField_givaro
+                    from sage.rings.finite_rings.residue_field_givaro import ResidueFiniteField_givaro
                 except ImportError:
                     if impl is not None:
                         raise
@@ -470,7 +470,7 @@ class ResidueFieldFactory(UniqueFactory):
                     return ResidueFiniteField_givaro(p, q, names, f, to_vs, to_order, PB)
             elif q % 2 == 0 and (impl is None or impl == 'ntl'):
                 try:
-                    from .residue_field_ntl_gf2e import ResidueFiniteField_ntl_gf2e
+                    from sage.rings.finite_rings.residue_field_ntl_gf2e import ResidueFiniteField_ntl_gf2e
                 except ImportError:
                     if impl is not None:
                         raise
@@ -478,7 +478,7 @@ class ResidueFieldFactory(UniqueFactory):
                     return ResidueFiniteField_ntl_gf2e(q, names, f, "poly", p, to_vs, to_order, PB)
             if impl is None or impl == 'pari':
                 try:
-                    from .residue_field_pari_ffelt import ResidueFiniteField_pari_ffelt
+                    from sage.rings.finite_rings.residue_field_pari_ffelt import ResidueFiniteField_pari_ffelt
                 except ImportError:
                     if impl is not None:
                         raise
diff --git a/src/sage/rings/function_field/element.pyx b/src/sage/rings/function_field/element.pyx
index dceaa85fd2e..93a0333a14c 100644
--- a/src/sage/rings/function_field/element.pyx
+++ b/src/sage/rings/function_field/element.pyx
@@ -83,7 +83,7 @@ def is_FunctionFieldElement(x):
     """
     if isinstance(x, FunctionFieldElement):
         return True
-    from .function_field import is_FunctionField
+    from sage.rings.function_field.function_field import is_FunctionField
     return is_FunctionField(x.parent())
 
 def make_FunctionFieldElement(parent, element_class, representing_element):
diff --git a/src/sage/rings/function_field/element_polymod.pyx b/src/sage/rings/function_field/element_polymod.pyx
index 5e748b22a6f..c6fdea83b09 100644
--- a/src/sage/rings/function_field/element_polymod.pyx
+++ b/src/sage/rings/function_field/element_polymod.pyx
@@ -385,7 +385,7 @@ cdef class FunctionFieldElement_polymod(FunctionFieldElement):
         if deg == 1:
             return self._parent(self._x[0].nth_root(self._parent.characteristic()))
 
-        from .function_field_rational import RationalFunctionField
+        from sage.rings.function_field.function_field_rational import RationalFunctionField
         if not isinstance(self.base_ring(), RationalFunctionField):
             raise NotImplementedError("only implemented for simple extensions of function fields")
         # compute a representation of the generator y of the field in terms of powers of y^p
diff --git a/src/sage/rings/function_field/element_rational.pyx b/src/sage/rings/function_field/element_rational.pyx
index 0b36c50f5f7..986a46300b8 100644
--- a/src/sage/rings/function_field/element_rational.pyx
+++ b/src/sage/rings/function_field/element_rational.pyx
@@ -302,7 +302,7 @@ cdef class FunctionFieldElement_rational(FunctionFieldElement):
             sage: (1/x^2).valuation(p)                                                  # needs sage.libs.pari
             -2
         """
-        from .place import FunctionFieldPlace
+        from sage.rings.function_field.place import FunctionFieldPlace
 
         if not isinstance(place, FunctionFieldPlace):
             # place is an irreducible polynomial
diff --git a/src/sage/rings/integer.pyx b/src/sage/rings/integer.pyx
index bd31ccbb31d..c990c200e57 100644
--- a/src/sage/rings/integer.pyx
+++ b/src/sage/rings/integer.pyx
@@ -2536,7 +2536,7 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
         cdef int pow_2
         cdef size_t upper,lower,middle
 
-        from .real_mpfi import RIF as R
+        from sage.rings.real_mpfi import RIF as R
 
         rif_self = R(self)
 
@@ -2722,7 +2722,7 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
                 # (suggested by David Harvey and Carl Witty)
                 # "for randomly distributed integers, the chance of this
                 # interval-based comparison failing is absurdly low"
-                from .real_mpfi import RIF
+                from sage.rings.real_mpfi import RIF
                 approx_compare = RIF(m)**guess
                 if self > approx_compare:
                     guess_filled = 1
diff --git a/src/sage/rings/morphism.pyx b/src/sage/rings/morphism.pyx
index f8e32bd8c62..a9cb8eda29e 100644
--- a/src/sage/rings/morphism.pyx
+++ b/src/sage/rings/morphism.pyx
@@ -650,7 +650,7 @@ cdef class RingHomomorphism(RingMap):
             True
 
         """
-        from .homset import RingHomset_generic
+        from sage.rings.homset import RingHomset_generic
         if not isinstance(parent, RingHomset_generic):
             raise TypeError("parent must be a ring homset")
         RingMap.__init__(self, parent)
@@ -1038,10 +1038,10 @@ cdef class RingHomomorphism(RingMap):
             sage: f.kernel()                                                            # needs sage.libs.singular
             Ideal (0) of Multivariate Polynomial Ring in t, u over Rational Field
         """
-        from .polynomial.polynomial_quotient_ring import is_PolynomialQuotientRing
-        from .quotient_ring import is_QuotientRing
-        from .polynomial.multi_polynomial_ring import is_MPolynomialRing
-        from .polynomial.polynomial_ring import is_PolynomialRing
+        from sage.rings.polynomial.polynomial_quotient_ring import is_PolynomialQuotientRing
+        from sage.rings.quotient_ring import is_QuotientRing
+        from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
+        from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
         B = self.codomain()
         graph, from_B, to_A = self._graph_ideal()
         Q = graph.ring()
@@ -1287,8 +1287,8 @@ cdef class RingHomomorphism(RingMap):
             ...
             NotImplementedError: rings are not commutative
         """
-        from .quotient_ring import is_QuotientRing
-        from .ideal import Ideal_generic
+        from sage.rings.quotient_ring import is_QuotientRing
+        from sage.rings.ideal import Ideal_generic
         A = self.domain()
         B = self.codomain()
         if not (A.is_commutative() and B.is_commutative()):
@@ -2882,7 +2882,7 @@ cdef class FrobeniusEndomorphism_generic(RingHomomorphism):
             Frobenius endomorphism x |--> x^(5^2) of Power Series Ring in u
              over Finite Field of size 5
         """
-        from .ring import CommutativeRing
+        from sage.rings.ring import CommutativeRing
         from sage.categories.homset import Hom
         if not isinstance(domain, CommutativeRing):
             raise TypeError("The base ring must be a commutative ring")
@@ -3135,14 +3135,14 @@ def _tensor_product_ring(B, A):
         ...
         ValueError: term ordering must be global
     """
-    from .finite_rings.finite_field_base import FiniteField
-    from .number_field.number_field_base import NumberField
-    from .polynomial.multi_polynomial_ring import is_MPolynomialRing
-    from .polynomial.polynomial_quotient_ring import is_PolynomialQuotientRing
-    from .polynomial.polynomial_ring import is_PolynomialRing
-    from .polynomial.polynomial_ring_constructor import PolynomialRing
-    from .polynomial.term_order import TermOrder
-    from .quotient_ring import is_QuotientRing
+    from sage.rings.finite_rings.finite_field_base import FiniteField
+    from sage.rings.number_field.number_field_base import NumberField
+    from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
+    from sage.rings.polynomial.polynomial_quotient_ring import is_PolynomialQuotientRing
+    from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
+    from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
+    from sage.rings.polynomial.term_order import TermOrder
+    from sage.rings.quotient_ring import is_QuotientRing
 
     if set(B.variable_names()).isdisjoint(A.variable_names()):
         names = B.variable_names() + A.variable_names()
diff --git a/src/sage/rings/number_field/number_field_element.pyx b/src/sage/rings/number_field/number_field_element.pyx
index a0553fc31d9..a21d22e43a4 100644
--- a/src/sage/rings/number_field/number_field_element.pyx
+++ b/src/sage/rings/number_field/number_field_element.pyx
@@ -353,7 +353,7 @@ cdef class NumberFieldElement(NumberFieldElement_base):
           quadratic field elements)
         """
         if check:
-            from .number_field import NumberField_cyclotomic
+            from sage.rings.number_field.number_field import NumberField_cyclotomic
             if not isinstance(self.number_field(), NumberField_cyclotomic) \
                or not isinstance(new_parent, NumberField_cyclotomic):
                 raise TypeError("The field and the new parent field must both be cyclotomic fields.")
@@ -523,7 +523,7 @@ cdef class NumberFieldElement(NumberFieldElement_base):
             return str(self)
         p = self.polynomial()
         P = self.parent()
-        from .number_field import NumberField_cyclotomic
+        from sage.rings.number_field.number_field import NumberField_cyclotomic
         if isinstance(P, NumberField_cyclotomic):
             n = P._n()
             if n != 2 and n % 4 == 2:
@@ -564,7 +564,7 @@ cdef class NumberFieldElement(NumberFieldElement_base):
             ....:         t = K.random_element()
             ....:         assert K(libgap(t)) == t, "n = {}  t = {}".format(n,t)
         """
-        from .number_field import NumberField_cyclotomic
+        from sage.rings.number_field.number_field import NumberField_cyclotomic
         P = self.parent()
         if not isinstance(P, NumberField_cyclotomic):
             raise NotImplementedError("libgap conversion is only implemented for cyclotomic fields")
@@ -1991,7 +1991,7 @@ cdef class NumberFieldElement(NumberFieldElement_base):
             raise ArithmeticError("factorization of 0 is not defined")
 
         K = self.parent()
-        from .order import is_NumberFieldOrder
+        from sage.rings.number_field.order import is_NumberFieldOrder
         if is_NumberFieldOrder(K):
             K = K.number_field()
         fac = K.ideal(self).factor()
@@ -2097,7 +2097,7 @@ cdef class NumberFieldElement(NumberFieldElement_base):
         if R.is_field():
             return R.one()
 
-        from .order import is_NumberFieldOrder
+        from sage.rings.number_field.order import is_NumberFieldOrder
         if not is_NumberFieldOrder(R) or not R.is_maximal():
             raise NotImplementedError("gcd() for %r is not implemented" % R)
 
@@ -2886,7 +2886,7 @@ cdef class NumberFieldElement(NumberFieldElement_base):
             raise ValueError("need a real or complex embedding to convert "
                              "a non rational element of a number field "
                              "into an algebraic number")
-        from .number_field import refine_embedding
+        from sage.rings.number_field.number_field import refine_embedding
         emb = refine_embedding(emb, infinity)
         return parent(emb(self))
 
@@ -2999,7 +2999,7 @@ cdef class NumberFieldElement(NumberFieldElement_base):
         if embedding is None:
             raise TypeError("an embedding into RR or CC must be specified")
 
-        from .number_field import NumberField_cyclotomic
+        from sage.rings.number_field.number_field import NumberField_cyclotomic
         if isinstance(K, NumberField_cyclotomic):
             # solution by radicals may be difficult, but we have a closed form
             from sage.functions.log import exp
@@ -3011,7 +3011,7 @@ cdef class NumberFieldElement(NumberFieldElement_base):
             gen_image = exp(k*two_pi_i/K._n())
             return self.polynomial()(gen_image)
         else:
-            from .number_field import refine_embedding
+            from sage.rings.number_field.number_field import refine_embedding
             # Convert the embedding to an embedding into AA or QQbar
             embedding = refine_embedding(embedding, infinity)
             a = embedding(self).radical_expression()
@@ -3365,7 +3365,7 @@ cdef class NumberFieldElement(NumberFieldElement_base):
             True
         """
         if self.__multiplicative_order is None:
-            from .number_field import NumberField_cyclotomic
+            from sage.rings.number_field.number_field import NumberField_cyclotomic
             if self.is_rational():
                 if self.is_one():
                     self.__multiplicative_order = ZZ.one()
@@ -3923,7 +3923,7 @@ cdef class NumberFieldElement(NumberFieldElement_base):
             ...
             ValueError: P must be prime
         """
-        from .number_field_ideal import is_NumberFieldIdeal
+        from sage.rings.number_field.number_field_ideal import is_NumberFieldIdeal
         if not is_NumberFieldIdeal(P):
             if isinstance(P, NumberFieldElement):
                 P = self.number_field().fractional_ideal(P)
diff --git a/src/sage/rings/number_field/number_field_element_quadratic.pyx b/src/sage/rings/number_field/number_field_element_quadratic.pyx
index 3cdaabb3140..88118848cc8 100644
--- a/src/sage/rings/number_field/number_field_element_quadratic.pyx
+++ b/src/sage/rings/number_field/number_field_element_quadratic.pyx
@@ -520,7 +520,7 @@ cdef class NumberFieldElement_quadratic(NumberFieldElement_absolute):
         - Craig Citro (reworked for quadratic elements)
         """
         if check:
-            from .number_field import NumberField_cyclotomic
+            from sage.rings.number_field.number_field import NumberField_cyclotomic
             if not isinstance(self.number_field(), NumberField_cyclotomic) \
                    or not isinstance(new_parent, NumberField_cyclotomic):
                 raise TypeError("The field and the new parent field must both be cyclotomic fields.")
@@ -1918,10 +1918,10 @@ cdef class NumberFieldElement_quadratic(NumberFieldElement_absolute):
         else:
             # avoid circular import
             if self._parent._embedding is None:
-                from .number_field import NumberField
+                from sage.rings.number_field.number_field import NumberField
                 K = NumberField(QQ['x'].gen()**2 - negD, 'sqrt%s' % negD)
             else:
-                from .number_field import QuadraticField
+                from sage.rings.number_field.number_field import QuadraticField
                 K = QuadraticField(negD, 'sqrt%s' % negD)
             q = (<NumberFieldElement_quadratic> K._zero_element)._new()
             mpz_set(q.denom, self.denom)
diff --git a/src/sage/rings/number_field/number_field_morphisms.pyx b/src/sage/rings/number_field/number_field_morphisms.pyx
index 1f6e12ce2c5..38a8dfd3726 100644
--- a/src/sage/rings/number_field/number_field_morphisms.pyx
+++ b/src/sage/rings/number_field/number_field_morphisms.pyx
@@ -616,7 +616,7 @@ cdef class CyclotomicFieldEmbedding(NumberFieldEmbedding):
             -1
         """
         Morphism.__init__(self, K, L)
-        from .number_field import NumberField_cyclotomic
+        from sage.rings.number_field.number_field import NumberField_cyclotomic
         if not isinstance(K, NumberField_cyclotomic) or not isinstance(L, NumberField_cyclotomic):
             raise TypeError("CyclotomicFieldEmbedding only valid for cyclotomic fields.")
         Kn = K._n()
diff --git a/src/sage/rings/number_field/totallyreal_data.pyx b/src/sage/rings/number_field/totallyreal_data.pyx
index e504fb6b45f..9bce936b362 100644
--- a/src/sage/rings/number_field/totallyreal_data.pyx
+++ b/src/sage/rings/number_field/totallyreal_data.pyx
@@ -440,7 +440,7 @@ def easy_is_irreducible_py(f):
 cdef double eps_global
 eps_global = 10.**(-4)
 
-from .totallyreal_phc import __lagrange_bounds_phc
+from sage.rings.number_field.totallyreal_phc import __lagrange_bounds_phc
 
 cdef class tr_data:
     r"""
diff --git a/src/sage/rings/padics/morphism.pyx b/src/sage/rings/padics/morphism.pyx
index 3dbae06bc51..a50c92a06f9 100644
--- a/src/sage/rings/padics/morphism.pyx
+++ b/src/sage/rings/padics/morphism.pyx
@@ -21,7 +21,7 @@ from sage.structure.richcmp cimport (richcmp, rich_to_bool,
                                      richcmp_not_equal)
 
 from sage.rings.morphism cimport RingHomomorphism
-from .padic_generic import pAdicGeneric
+from sage.rings.padics.padic_generic import pAdicGeneric
 
 
 cdef class FrobeniusEndomorphism_padics(RingHomomorphism):
diff --git a/src/sage/rings/padics/padic_printing.pyx b/src/sage/rings/padics/padic_printing.pyx
index caf19c7bdf9..f92afb51529 100644
--- a/src/sage/rings/padics/padic_printing.pyx
+++ b/src/sage/rings/padics/padic_printing.pyx
@@ -464,7 +464,7 @@ cdef class pAdicPrinter_class(SageObject):
                 raise ValueError("max_terse_terms must be positive and fit in a long")
         else:
             self.max_terse_terms = _printer_defaults._max_terse_terms
-        from .factory import _canonicalize_show_prec
+        from sage.rings.padics.factory import _canonicalize_show_prec
         self.show_prec = _canonicalize_show_prec(self.ring._prec_type(), mode, show_prec)
 
         # Incompatibilities
diff --git a/src/sage/rings/padics/pow_computer.pyx b/src/sage/rings/padics/pow_computer.pyx
index 83aa163d36b..942b2a6323e 100644
--- a/src/sage/rings/padics/pow_computer.pyx
+++ b/src/sage/rings/padics/pow_computer.pyx
@@ -624,13 +624,13 @@ cdef PowComputer_base PowComputer_c(Integer m, Integer cache_limit, Integer prec
         if PC is not None:
             return PC
     if prec_type == 'capped-rel':
-        from .padic_capped_relative_element import PowComputer_ as PC_class
+        from sage.rings.padics.padic_capped_relative_element import PowComputer_ as PC_class
     elif prec_type == 'capped-abs':
-        from .padic_capped_absolute_element import PowComputer_ as PC_class
+        from sage.rings.padics.padic_capped_absolute_element import PowComputer_ as PC_class
     elif prec_type == 'fixed-mod':
-        from .padic_fixed_mod_element import PowComputer_ as PC_class
+        from sage.rings.padics.padic_fixed_mod_element import PowComputer_ as PC_class
     elif prec_type == 'floating-point':
-        from .padic_floating_point_element import PowComputer_ as PC_class
+        from sage.rings.padics.padic_floating_point_element import PowComputer_ as PC_class
     else:
         PC_class = PowComputer_base
     PC = PC_class(m, mpz_get_ui(cache_limit.value), mpz_get_ui(prec_cap.value), mpz_get_ui(prec_cap.value), in_field)
diff --git a/src/sage/rings/padics/pow_computer_flint.pyx b/src/sage/rings/padics/pow_computer_flint.pyx
index 6d0837f7ee5..2ef7ff9e879 100644
--- a/src/sage/rings/padics/pow_computer_flint.pyx
+++ b/src/sage/rings/padics/pow_computer_flint.pyx
@@ -641,13 +641,13 @@ def PowComputer_flint_maker(prime, cache_limit, prec_cap, ram_prec_cap, in_field
 
     """
     if prec_type == 'capped-rel':
-        from .qadic_flint_CR import PowComputer_
+        from sage.rings.padics.qadic_flint_CR import PowComputer_
     elif prec_type == 'capped-abs':
-        from .qadic_flint_CA import PowComputer_
+        from sage.rings.padics.qadic_flint_CA import PowComputer_
     elif prec_type == 'fixed-mod':
-        from .qadic_flint_FM import PowComputer_
+        from sage.rings.padics.qadic_flint_FM import PowComputer_
     elif prec_type == 'floating-point':
-        from .qadic_flint_FP import PowComputer_
+        from sage.rings.padics.qadic_flint_FP import PowComputer_
     else:
         raise ValueError("unknown prec_type `%s`" % prec_type)
     return PowComputer_(prime, cache_limit, prec_cap, ram_prec_cap, in_field, poly)
diff --git a/src/sage/rings/polynomial/evaluation.pxd b/src/sage/rings/polynomial/evaluation.pxd
index 4978e83a831..bbd1ba97b4b 100644
--- a/src/sage/rings/polynomial/evaluation.pxd
+++ b/src/sage/rings/polynomial/evaluation.pxd
@@ -1,2 +1,2 @@
-from .evaluation_flint cimport *
-from .evaluation_ntl cimport *
+from sage.rings.polynomial.evaluation_flint cimport *
+from sage.rings.polynomial.evaluation_ntl cimport *
diff --git a/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx b/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
index e9787a2e0f7..561136bac6d 100644
--- a/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
+++ b/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
@@ -253,7 +253,7 @@ from sage.misc.sage_eval import sage_eval
 import sage.rings.polynomial.polynomial_singular_interface
 
 cimport cypari2.gen
-from . import polynomial_element
+from sage.rings.polynomial import polynomial_element
 
 permstore=[]
 cdef class MPolynomialRing_libsingular(MPolynomialRing_base):
diff --git a/src/sage/rings/polynomial/multi_polynomial_ring_base.pyx b/src/sage/rings/polynomial/multi_polynomial_ring_base.pyx
index 66ade555385..44946845b83 100644
--- a/src/sage/rings/polynomial/multi_polynomial_ring_base.pyx
+++ b/src/sage/rings/polynomial/multi_polynomial_ring_base.pyx
@@ -22,9 +22,9 @@ from sage.arith.misc import binomial
 
 from sage.rings.integer_ring import ZZ
 
-from . import polynomial_ring
-from .term_order import TermOrder
-from .polynomial_ring_constructor import (PolynomialRing,
+from sage.rings.polynomial import polynomial_ring
+from sage.rings.polynomial.term_order import TermOrder
+from sage.rings.polynomial.polynomial_ring_constructor import (PolynomialRing,
                                           polynomial_default_category)
 
 
@@ -135,7 +135,7 @@ cdef class MPolynomialRing_base(sage.rings.ring.CommutativeRing):
         """
         base = self.base_ring()
         if is_MPolynomialRing(base) or polynomial_ring.is_PolynomialRing(base):
-            from .flatten import FlatteningMorphism
+            from sage.rings.polynomial.flatten import FlatteningMorphism
             return FlatteningMorphism(self)
         else:
             return IdentityMorphism(self)
@@ -157,7 +157,7 @@ cdef class MPolynomialRing_base(sage.rings.ring.CommutativeRing):
             False
 
         """
-        from .polynomial_ring_constructor import PolynomialRing
+        from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
         from sage.categories.pushout import MultiPolynomialFunctor
         return MultiPolynomialFunctor(self.variable_names(), self.term_order()), self.base_ring()
 
@@ -323,7 +323,7 @@ cdef class MPolynomialRing_base(sage.rings.ring.CommutativeRing):
             vars.remove(str(v))
         if len(vars) == 0:
             return self.base_ring()
-        from .polynomial_ring_constructor import PolynomialRing
+        from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
         if order is None:
             try:
                 return PolynomialRing(self.base_ring(), vars,
@@ -614,7 +614,7 @@ cdef class MPolynomialRing_base(sage.rings.ring.CommutativeRing):
         a dict with respect to ``self.variable_names()``.
         """
         # This is probably horribly inefficient
-        from .polydict import ETuple
+        from sage.rings.polynomial.polydict import ETuple
         other_vars = list(x.parent().variable_names())
         name_mapping = [(other_vars.index(var) if var in other_vars else -1) for var in self.variable_names()]
         K = self.base_ring()
@@ -705,7 +705,7 @@ cdef class MPolynomialRing_base(sage.rings.ring.CommutativeRing):
         return "%s[%s]" % (sage.misc.latex.latex(self.base_ring()), vars)
 
     def _ideal_class_(self, n=0):
-        from .multi_polynomial_ideal import MPolynomialIdeal
+        from sage.rings.polynomial.multi_polynomial_ideal import MPolynomialIdeal
         return MPolynomialIdeal
 
     def _is_valid_homomorphism_(self, codomain, im_gens, base_map=None):
@@ -915,7 +915,7 @@ cdef class MPolynomialRing_base(sage.rings.ring.CommutativeRing):
         elif not set(my_vars).issubset(set(vars)):
             while my_vars[-1] in vars:
                 my_vars.pop()
-            from .polynomial_ring_constructor import PolynomialRing
+            from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
             return PolynomialRing(self.base_ring(), my_vars)
         else:
             try:
@@ -1357,7 +1357,7 @@ cdef class MPolynomialRing_base(sage.rings.ring.CommutativeRing):
         if order is None:
             order = self.term_order()
 
-        from .polynomial_ring_constructor import PolynomialRing
+        from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
         return PolynomialRing(base_ring, self.ngens(), names, order=order)
 
     def monomial(self, *exponents):
@@ -1786,11 +1786,11 @@ cdef class BooleanPolynomialRing_base(MPolynomialRing_base):
 # Leave *all* old versions!
 
 def unpickle_MPolynomialRing_generic_v1(base_ring, n, names, order):
-    from .polynomial_ring_constructor import PolynomialRing
+    from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
     return PolynomialRing(base_ring, n, names=names, order=order)
 
 
 def unpickle_MPolynomialRing_generic(base_ring, n, names, order):
-    from .polynomial_ring_constructor import PolynomialRing
+    from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 
     return PolynomialRing(base_ring, n, names=names, order=order)
diff --git a/src/sage/rings/polynomial/polynomial_number_field.pyx b/src/sage/rings/polynomial/polynomial_number_field.pyx
index 96f1c002e99..5bd458e5d12 100644
--- a/src/sage/rings/polynomial/polynomial_number_field.pyx
+++ b/src/sage/rings/polynomial/polynomial_number_field.pyx
@@ -72,7 +72,7 @@ We can also construct polynomials over relative number fields::
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-from .polynomial_element_generic import Polynomial_generic_dense_field
+from sage.rings.polynomial.polynomial_element_generic import Polynomial_generic_dense_field
 from sage.rings.rational_field import QQ
 from sage.structure.element import coerce_binop
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
diff --git a/src/sage/rings/power_series_ring_element.pyx b/src/sage/rings/power_series_ring_element.pyx
index 8f570db774a..31206e347f9 100644
--- a/src/sage/rings/power_series_ring_element.pyx
+++ b/src/sage/rings/power_series_ring_element.pyx
@@ -2957,7 +2957,7 @@ def _solve_linear_de(R, N, L, a, b, f0):
 def make_powerseries_poly_v0(parent,  f, prec, is_gen):
     # This is only used to unpickle old pickles. The new pickling
     # works differently!
-    from . import power_series_poly
+    from sage.rings import power_series_poly
     return power_series_poly.PowerSeries_poly(parent, f, prec, 0, is_gen)
 
 
diff --git a/src/sage/rings/rational.pyx b/src/sage/rings/rational.pyx
index 63ad2b36bee..150e4a523bd 100644
--- a/src/sage/rings/rational.pyx
+++ b/src/sage/rings/rational.pyx
@@ -1749,7 +1749,7 @@ cdef class Rational(sage.structure.element.FieldElement):
             return (self > 0)
 
         ## Check that p is prime
-        from .integer_ring import ZZ
+        from sage.rings.integer_ring import ZZ
         p = ZZ(p)
         if check and not p.is_prime():
             raise ValueError('p must be "infinity" or a positive prime number.')
@@ -4094,8 +4094,8 @@ cdef class Z_to_Q(Morphism):
               From: Integer Ring
               To:   Rational Field
         """
-        from . import integer_ring
-        from . import rational_field
+        from sage.rings import integer_ring
+        from sage.rings import rational_field
         import sage.categories.homset
         Morphism.__init__(self, sage.categories.homset.Hom(integer_ring.ZZ, rational_field.QQ))
 
@@ -4215,7 +4215,7 @@ cdef class int_to_Q(Morphism):
               From: Set of Python objects of class 'int'
               To:   Rational Field
         """
-        from . import rational_field
+        from sage.rings import rational_field
         import sage.categories.homset
         from sage.sets.pythonclass import Set_PythonType
         Morphism.__init__(self, sage.categories.homset.Hom(
diff --git a/src/sage/rings/real_double.pyx b/src/sage/rings/real_double.pyx
index f1e5eb0a2c8..19c9501bcf8 100644
--- a/src/sage/rings/real_double.pyx
+++ b/src/sage/rings/real_double.pyx
@@ -327,9 +327,9 @@ cdef class RealDoubleField_class(sage.rings.abc.RealDoubleField):
         if S is int or S is float:
             return ToRDF(S)
 
-        from .rational_field import QQ
+        from sage.rings.rational_field import QQ
         try:
-            from .real_lazy import RLF
+            from sage.rings.real_lazy import RLF
         except ImportError:
             RLF = None
 
@@ -349,7 +349,7 @@ cdef class RealDoubleField_class(sage.rings.abc.RealDoubleField):
                 return None
 
         try:
-            from .real_mpfr import RR
+            from sage.rings.real_mpfr import RR
         except ImportError:
             pass
         else:
@@ -431,7 +431,7 @@ cdef class RealDoubleField_class(sage.rings.abc.RealDoubleField):
         if prec == 53:
             return self
         else:
-            from .real_mpfr import RealField
+            from sage.rings.real_mpfr import RealField
             return RealField(prec)
 
 
@@ -979,7 +979,7 @@ cdef class RealDoubleElement(FieldElement):
             sage: mathematica(RDF(1e-25))  # optional - mathematica
             1.*^-25
         """
-        from .real_mpfr import RR
+        from sage.rings.real_mpfr import RR
         return RR(self._value)._mathematica_init_()
 
     def _sage_input_(self, sib, coerced):
@@ -2069,7 +2069,7 @@ def is_RealDoubleElement(x):
 cdef RealDoubleElement global_dummy_element
 
 try:
-    from .real_double_element_gsl import RealDoubleElement_gsl
+    from sage.rings.real_double_element_gsl import RealDoubleElement_gsl
 except ImportError:
     global_dummy_element = RealDoubleElement(0)
 else:
@@ -2175,7 +2175,7 @@ cdef void fast_tp_dealloc(PyObject* o) noexcept:
 from sage.misc.allocator cimport hook_tp_functions, hook_tp_functions_type
 hook_tp_functions(global_dummy_element, <newfunc>(&fast_tp_new), <destructor>(&fast_tp_dealloc), False)
 try:
-    from .real_double_element_gsl import RealDoubleElement_gsl
+    from sage.rings.real_double_element_gsl import RealDoubleElement_gsl
 except Exception:
     pass
 else:
diff --git a/src/sage/rings/real_double_element_gsl.pyx b/src/sage/rings/real_double_element_gsl.pyx
index 3ebb703b367..05346073d08 100644
--- a/src/sage/rings/real_double_element_gsl.pyx
+++ b/src/sage/rings/real_double_element_gsl.pyx
@@ -216,10 +216,10 @@ cdef class RealDoubleElement_gsl(RealDoubleElement):
 
     cdef _log_base(self, double log_of_base) noexcept:
         if self._value == 0:
-            from .real_double import RDF
+            from sage.rings.real_double import RDF
             return RDF(-1)/RDF(0)
         elif self._value < 0:
-            from .real_double import RDF
+            from sage.rings.real_double import RDF
             return RDF.NaN()
         sig_on()
         a = self._new_c(gsl_sf_log(self._value) / log_of_base)
diff --git a/src/sage/rings/real_mpfr.pyx b/src/sage/rings/real_mpfr.pyx
index d98a977d935..6eee51b444c 100644
--- a/src/sage/rings/real_mpfr.pyx
+++ b/src/sage/rings/real_mpfr.pyx
@@ -727,9 +727,9 @@ cdef class RealField_class(sage.rings.abc.RealField):
             sage: R.get_action(ZZ)
             Right scalar multiplication by Integer Ring on Univariate Polynomial Ring in x over Real Field with 53 bits of precision
         """
-        from .integer_ring import ZZ
-        from .rational_field import QQ
-        from .real_double import RDF
+        from sage.rings.integer_ring import ZZ
+        from sage.rings.rational_field import QQ
+        from sage.rings.real_double import RDF
 
         if S is ZZ:
             return ZZtoRR(ZZ, self)
@@ -1831,7 +1831,7 @@ cdef class RealNumber(sage.structure.element.RingElement):
             sage: RealField(100)(2).imag()
             0
         """
-        from .integer_ring import ZZ
+        from sage.rings.integer_ring import ZZ
 
         return ZZ(0)
 
@@ -2345,7 +2345,7 @@ cdef class RealNumber(sage.structure.element.RingElement):
         if have_same_parent(left, right):
             return (<RealNumber> left)._add_(right)
         try:
-            from .real_mpfi import RealIntervalFieldElement
+            from sage.rings.real_mpfi import RealIntervalFieldElement
         except ImportError:
             RealIntervalFieldElement = None
         if type(right) is RealIntervalFieldElement:
@@ -2369,7 +2369,7 @@ cdef class RealNumber(sage.structure.element.RingElement):
         if have_same_parent(left, right):
             return (<RealNumber> left)._sub_(right)
         try:
-            from .real_mpfi import RealIntervalFieldElement
+            from sage.rings.real_mpfi import RealIntervalFieldElement
         except ImportError:
             RealIntervalFieldElement = None
         if type(right) is RealIntervalFieldElement:
@@ -2393,7 +2393,7 @@ cdef class RealNumber(sage.structure.element.RingElement):
         if have_same_parent(left, right):
             return (<RealNumber> left)._mul_(right)
         try:
-            from .real_mpfi import RealIntervalFieldElement
+            from sage.rings.real_mpfi import RealIntervalFieldElement
         except ImportError:
             RealIntervalFieldElement = None
         if type(right) is RealIntervalFieldElement:
@@ -2417,7 +2417,7 @@ cdef class RealNumber(sage.structure.element.RingElement):
         if have_same_parent(left, right):
             return (<RealNumber> left)._div_(right)
         try:
-            from .real_mpfi import RealIntervalFieldElement
+            from sage.rings.real_mpfi import RealIntervalFieldElement
         except ImportError:
             RealIntervalFieldElement = None
         if type(right) is RealIntervalFieldElement:
@@ -3628,7 +3628,7 @@ cdef class RealNumber(sage.structure.element.RingElement):
         if mpfr_zero_p(self.value):
             return Rational(0)
 
-        from .real_mpfi import RealIntervalField
+        from sage.rings.real_mpfi import RealIntervalField
 
         cdef mpfr_rnd_t rnd = (<RealField_class>self._parent).rnd
         cdef mpfr_prec_t prec = (<RealField_class>self._parent)._prec
@@ -3748,7 +3748,7 @@ cdef class RealNumber(sage.structure.element.RingElement):
             raise ValueError('Must specify exactly one of max_error or max_denominator in nearby_rational()')
 
         if max_error is not None:
-            from .real_mpfi import RealIntervalField
+            from sage.rings.real_mpfi import RealIntervalField
 
             intv_field = RealIntervalField(self.prec())
             intv = intv_field(self - max_error, self + max_error)
@@ -5575,7 +5575,7 @@ cdef class RealNumber(sage.structure.element.RingElement):
         # If we got here, then we're not a perfect power of a boundary
         # point, so it's safe to use the interval arithmetic technique.
 
-        from .real_mpfi import RealIntervalField
+        from sage.rings.real_mpfi import RealIntervalField
 
         cdef mpfr_prec_t prec = fld._prec + 10
 
diff --git a/src/sage/rings/ring.pyx b/src/sage/rings/ring.pyx
index 75f58656385..71e72f4f45c 100644
--- a/src/sage/rings/ring.pyx
+++ b/src/sage/rings/ring.pyx
@@ -1447,7 +1447,7 @@ cdef class CommutativeRing(Ring):
             sage: f(1+u)
             1 + u^25
         """
-        from .morphism import FrobeniusEndomorphism_generic
+        from sage.rings.morphism import FrobeniusEndomorphism_generic
         return FrobeniusEndomorphism_generic(self, n)
 
     def derivation_module(self, codomain=None, twist=None):
diff --git a/src/sage/sat/solvers/satsolver.pyx b/src/sage/sat/solvers/satsolver.pyx
index 83735c86989..04b9c95f089 100644
--- a/src/sage/sat/solvers/satsolver.pyx
+++ b/src/sage/sat/solvers/satsolver.pyx
@@ -390,16 +390,16 @@ def SAT(solver=None, *args, **kwds):
         from sage.sat.solvers.picosat import PicoSAT
         return PicoSAT(*args, **kwds)
     elif solver == "LP":
-        from .sat_lp import SatLP
+        from sage.sat.solvers.sat_lp import SatLP
         return SatLP()
     elif solver == 'glucose':
-        from .dimacs import Glucose
+        from sage.sat.solvers.dimacs import Glucose
         return Glucose(*args, **kwds)
     elif solver == 'glucose-syrup':
-        from .dimacs import GlucoseSyrup
+        from sage.sat.solvers.dimacs import GlucoseSyrup
         return GlucoseSyrup(*args, **kwds)
     elif solver == 'kissat':
-        from .dimacs import Kissat
+        from sage.sat.solvers.dimacs import Kissat
         return Kissat(*args, **kwds)
     else:
         raise ValueError("Solver '{}' is not available".format(solver))
diff --git a/src/sage/structure/parent.pyx b/src/sage/structure/parent.pyx
index 9a0cbd66b9a..6ac939db3c8 100644
--- a/src/sage/structure/parent.pyx
+++ b/src/sage/structure/parent.pyx
@@ -2672,7 +2672,7 @@ cdef class Parent(sage.structure.category_object.CategoryObject):
                 _register_pair(self, S, "action")  # avoid possible infinite loops
 
                 # detect actions defined by _rmul_, _lmul_, _act_on_, and _acted_upon_ methods
-                from .coerce_actions import detect_element_action
+                from sage.structure.coerce_actions import detect_element_action
                 action = detect_element_action(self, S, self_on_left, self_el, S_el)
                 if action is not None:
                     return action
diff --git a/src/sage/symbolic/expression.pyx b/src/sage/symbolic/expression.pyx
index 0b80c017a0b..9d86a81b24b 100644
--- a/src/sage/symbolic/expression.pyx
+++ b/src/sage/symbolic/expression.pyx
@@ -922,7 +922,7 @@ cdef class Expression(Expression_abc):
         if state[0] != 0 or len(state) != 3:
             raise ValueError("unknown state information")
         # set parent
-        from .ring import SR
+        from sage.symbolic.ring import SR
         self._parent = SR
         # get variables
         cdef GExList sym_lst
@@ -966,7 +966,7 @@ cdef class Expression(Expression_abc):
             True
 
         """
-        from .ring import SR
+        from sage.symbolic.ring import SR
         SR.cleanup_var(self)
         return False
 
@@ -3250,7 +3250,7 @@ cdef class Expression(Expression_abc):
             sage: x.is_trivially_equal(QQbar(1/2))
             True
         """
-        from .ring import SR
+        from sage.symbolic.ring import SR
         cdef Expression _other = <Expression>(SR(other))
         sig_on()
         try:
@@ -12130,7 +12130,7 @@ cdef class Expression(Expression_abc):
             ...
             ValueError: cannot convert
         """
-        from . import units
+        from sage.symbolic import units
         return units.convert(self, target)
 
     ###################################################################
diff --git a/src/sage/symbolic/function.pyx b/src/sage/symbolic/function.pyx
index 792d81ebcc9..e349fe20100 100644
--- a/src/sage/symbolic/function.pyx
+++ b/src/sage/symbolic/function.pyx
@@ -148,10 +148,10 @@ from sage.structure.richcmp cimport richcmp
 
 from sage.misc.fpickle import pickle_function, unpickle_function
 
-from .symbols import symbol_table, register_symbol
+from sage.symbolic.symbols import symbol_table, register_symbol
 
 try:
-    from .expression import (
+    from sage.symbolic.expression import (
         call_registered_function, find_registered_function, register_or_update_function,
         get_sfunction_from_hash, get_sfunction_from_serial as get_sfunction_from_serial
     )
@@ -528,7 +528,7 @@ cdef class Function(SageObject):
         # to a numeric type at the end
         symbolic_input = any(isinstance(arg, Expression) for arg in args)
 
-        from .ring import SR
+        from sage.symbolic.ring import SR
 
         if coerce:
             try:
@@ -606,7 +606,7 @@ cdef class Function(SageObject):
             sage: sin.default_variable()                                                # needs sage.symbolic
             x
         """
-        from .ring import SR
+        from sage.symbolic.ring import SR
         return SR.var('x')
 
     def _is_numerical(self, x):
@@ -1053,7 +1053,7 @@ cdef class BuiltinFunction(Function):
             if (self._preserved_arg
                     and isinstance(args[self._preserved_arg-1], Element)):
                 arg_parent = parent(args[self._preserved_arg-1])
-                from .ring import SR
+                from sage.symbolic.ring import SR
                 if arg_parent is SR:
                     return res
                 from sage.rings.polynomial.polynomial_ring import PolynomialRing_commutative
diff --git a/src/sage/symbolic/pynac_impl.pxi b/src/sage/symbolic/pynac_impl.pxi
index 88436ee2705..b2091522c49 100644
--- a/src/sage/symbolic/pynac_impl.pxi
+++ b/src/sage/symbolic/pynac_impl.pxi
@@ -70,7 +70,7 @@ cdef ex_to_pyExpression(GEx juice) noexcept:
     cdef Expression nex
     nex = <Expression>Expression.__new__(Expression)
     nex._gobj = GEx(juice)
-    from .ring import SR
+    from sage.symbolic.ring import SR
     nex._parent = SR
     return nex
 
@@ -189,7 +189,7 @@ cdef GEx pyExpression_to_ex(res) except *:
     """
     if res is None:
         raise TypeError("function returned None, expected return value of type sage.symbolic.expression.Expression")
-    from .ring import SR
+    from sage.symbolic.ring import SR
     try:
         t = SR.coerce(res)
     except TypeError as err:
@@ -1156,7 +1156,7 @@ cdef bint py_is_integer(x) noexcept:
     if not isinstance(x, Element):
         return False
     P = (<Element>x)._parent
-    from .ring import SymbolicRing
+    from sage.symbolic.ring import SymbolicRing
     return (isinstance(P, SymbolicRing) or P.is_exact()) and x in ZZ
 
 
@@ -1246,7 +1246,7 @@ cdef bint py_is_exact(x) noexcept:
     if not isinstance(x, Element):
         return False
     P = (<Element>x)._parent
-    from .ring import SymbolicRing
+    from sage.symbolic.ring import SymbolicRing
     return isinstance(P, SymbolicRing) or P.is_exact()
 
 
@@ -1553,7 +1553,7 @@ cdef py_step(n) noexcept:
     """
     Return step function of n.
     """
-    from .ring import SR
+    from sage.symbolic.ring import SR
     if n < 0:
         return SR(0)
     elif n > 0:
@@ -2466,7 +2466,7 @@ def init_pynac_I():
     from sage.rings.number_field.number_field import GaussianField
     pynac_I = GaussianField().gen()
     ginac_pyinit_I(pynac_I)
-    from .ring import SR
+    from sage.symbolic.ring import SR
     return new_Expression_from_GEx(SR, g_I)
 
 
diff --git a/src/sage/symbolic/ring.pyx b/src/sage/symbolic/ring.pyx
index f3f32b9c922..a74db5807d5 100644
--- a/src/sage/symbolic/ring.pyx
+++ b/src/sage/symbolic/ring.pyx
@@ -213,7 +213,7 @@ cdef class SymbolicRing(sage.rings.abc.SymbolicRing):
             from sage.rings.real_lazy import RLF, CLF
             from sage.rings.finite_rings.finite_field_base import FiniteField
 
-            from .subring import GenericSymbolicSubring
+            from sage.symbolic.subring import GenericSymbolicSubring
 
             if R._is_numerical():
                 # Almost anything with a coercion into any precision of CC
@@ -1133,7 +1133,7 @@ cdef class SymbolicRing(sage.rings.abc.SymbolicRing):
         """
         if self is not SR:
             raise NotImplementedError('cannot create subring of %s' % (self,))
-        from .subring import SymbolicSubring
+        from sage.symbolic.subring import SymbolicSubring
         return SymbolicSubring(*args, **kwds)
 
     def _fricas_init_(self):