Lemma 15.51.12. Properties (A), (B), (C), (D), and (E) hold for $P(k \to R) =$“$R$ is Cohen-Macaulay”.
Proof. Follows immediately from Lemma 15.51.11 and the fact that a Noetherian ring is Cohen-Macaulay if and only if it satisfies conditions $(S_ n)$ for all $n$. $\square$
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