Merge pull request #110 from fbielejec/main

fix the description

chapters/algebra-moonmath.tex

@@ -1185,7 +1185,7 @@ \subsection{Prime Field Extensions}\label{field-extension}
 \begin{remark}
 Similarly to the way prime fields $\F_p$ are generated by starting with the ring of integers and then dividing by a prime number $p$ and keeping the remainder, prime field extensions $\F_{p^m}$ are generated by starting with the ring $\F_p[x]$ of polynomials and then dividing them by an irreducible polynomial of degree $m$ and keeping the remainder.
 
-In fact, it can be shown that $\F_{p^m}$ is the set of all remainders when dividing any polynomial $Q\in \F_p[x]$ by an irreducible polynomial $P$ of degree $m$. This is analogous to how $\F_p$ is the set of all remainders when dividing integers by $p$.
+In fact, it can be shown that $\F_{p^m}$ is the set of all remainders when dividing all of the polynomials $Q\in \F_p[x]$ by an irreducible polynomial $P$ of degree $m$. This is analogous to how $\F_p$ is the set of all remainders when dividing integers by $p$.
 \end{remark}
 
 Any field $\F_{p^m}$ constructed in the above manner is a field extension of $\F_p$. To be more general, a field $\F_{p^{m_2}}$ is a field extension of a field $\F_{p^{m_1}}$ if and only if $m_1$ divides $m_2$. From this, we can deduce that, for any given fixed prime number, there are nested sequences of subfields whenever the power $m_j$ divides the power $m_{j+1}$: