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).
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
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: