Add "over" and some cosmetic changes

Thanks to Fred Rohrer
http://stacks.math.columbia.edu/tag/00LP#comment-139

algebra.tex

@@ -15161,16 +15161,16 @@ \section{Ext groups and depth}
 \label{lemma-resolution-by-finite-free}
 Let $R$ be a ring. Let $M$ be an $R$-module.
 \begin{enumerate}
-\item The exists an exact complex
+\item There exists an exact complex
 $$
 \ldots \to F_2 \to F_1 \to F_0 \to M \to 0.
 $$
 with $F_i$ free $R$-modules.
-\item If $R$ is Noetherian and $M$ finite $R$, then we
-choose the complex such that each $F_i$ is finite free.
-In other words, we may find an exact complex
+\item If $R$ is Noetherian and $M$ finite over $R$, then we
+can choose the complex such that $F_i$ is finite free.
+In other words, we can find an exact complex
 $$
-\ldots \to R^{n_2} \to R^{n_1} \to R^{n_0} \to M \to 0.
+\ldots \to R^{\oplus n_2} \to R^{\oplus n_1} \to R^{\oplus n_0} \to M \to 0.
 $$
 \end{enumerate}
 \end{lemma}