## Tag `00LC`

Chapter 10: Commutative Algebra > Section 10.62: Associated primes

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 14470–14475 (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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