# The Stacks Project

## Tag 00LC

Lemma 10.62.5. Let $R$ be a Noetherian ring. Let $M$ be a finite $R$-module. Then $\text{Ass}(M)$ is finite.

Proof. Immediate from Lemma 10.62.4 and Lemma 10.61.1. $\square$

The code snippet corresponding to this tag is a part of the file algebra.tex and is located in lines 14440–14445 (see updates for more information).

\begin{lemma}
\label{lemma-finite-ass}
Let $R$ be a Noetherian ring.
Let $M$ be a finite $R$-module.
Then $\text{Ass}(M)$ is finite.
\end{lemma}

\begin{proof}
Immediate from Lemma \ref{lemma-ass-filter} and
Lemma \ref{lemma-filter-Noetherian-module}.
\end{proof}

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