The Stacks project

Lemma 27.4.5. The following properties of a ring $R$ are local.

  1. (Cohen-Macaulay.) The ring $R$ is Noetherian and CM, see Algebra, Definition 10.103.6.

  2. (Regular.) The ring $R$ is Noetherian and regular, see Algebra, Definition 10.109.7.

  3. (Absolutely Noetherian.) The ring $R$ is of finite type over $Z$.

  4. Add more here as needed.1

Proof. Omitted. $\square$

[1] But we only list those properties here which we have not already dealt with separately somewhere else.

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