Processing math: 100%

The Stacks project

Lemma 10.104.4. Suppose R is a Noetherian local Cohen-Macaulay ring of dimension d. For any prime \mathfrak p \subset R we have

\dim (R) = \dim (R_{\mathfrak p}) + \dim (R/\mathfrak p).

Proof. Follows immediately from Lemma 10.104.3. (Also, this is a special case of Lemma 10.103.10.) \square


Comments (0)

There are also:

  • 7 comment(s) on Section 10.104: Cohen-Macaulay rings

Your email address will not be published.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.