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Improve statement Nakayama's lemma

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aisejohan committed Aug 5, 2018
1 parent a00296b commit 656b9f6c43a4b3712d72ca9059937dab7f58b674
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  1. +1 −1 algebra.tex
@@ -3395,7 +3395,7 @@ \section{Nakayama's lemma}
$fM = 0$.
\item If $IM = M$, $M$ is finite, and $I \subset \text{rad}(R)$, then $M = 0$.
\item If $N, N' \subset M$, $M = N + IN'$, and $N'$ is finite,
then there exists a $f \in 1 + I$ such that $M_f = N_f$.
then there exists a $f \in 1 + I$ such that $fM \subset N$ and $M_f = N_f$.
\item If $N, N' \subset M$, $M = N + IN'$, $N'$ is finite, and
$I \subset \text{rad}(R)$, then $M = N$.
\item If $N \to M$ is a module map, $N/IN \to M/IM$ is

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