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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 14473–14478 (see updates for more information).

    Let $R$ be a Noetherian ring.
    Let $M$ be a finite $R$-module.
    Then $\text{Ass}(M)$ is finite.
    Immediate from Lemma \ref{lemma-ass-filter} and
    Lemma \ref{lemma-filter-Noetherian-module}.

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