The Stacks project

Lemma 28.4.5. The following properties of a ring $R$ are local.

  1. (Cohen-Macaulay.) The ring $R$ is Noetherian and CM, see Algebra, Definition 10.104.6.

  2. (Regular.) The ring $R$ is Noetherian and regular, see Algebra, Definition 10.110.7.

  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.

Comments (2)

Post a comment

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.

In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 01OT. Beware of the difference between the letter 'O' and the digit '0'.