Lemma 10.103.6 (0AAD)—The Stacks project

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Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.103: Cohen-Macaulay modules
Lemma 10.103.6 (cite)

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Lemma 10.103.6. Let $R \to S$ be a surjective homomorphism of Noetherian local rings. Let $N$ be a finite $S$ -module. Then $N$ is Cohen-Macaulay as an $S$ -module if and only if $N$ is Cohen-Macaulay as an $R$ -module.

Proof. Omitted. $\square$

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