Lemma 10.104.7 (00ND)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.104: Cohen-Macaulay rings
Lemma 10.104.7 (cite)

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Lemma 10.104.7. Suppose $R$ is a Noetherian Cohen-Macaulay ring. Any polynomial algebra over $R$ is Cohen-Macaulay.

Proof. Special case of Lemma 10.103.13. $\square$

Comments (2)

Comment #2982 by Dario Weißmann on October 31, 2017 at 11:15

The lemma only holds for finite type polynomial algebras.

Comment #3106 by Johan on February 01, 2018 at 00:19

Well, I think that is what polynomial algebra means unless you specify "infinitely many variables". So I am going to leave as is for now.

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