Proof. Let $R$ be a regular ring. By Lemma 10.157.4 it suffices to prove that $R$ is $(R_1)$ and $(S_2)$. As a regular local ring is Cohen-Macaulay, see Lemma 10.106.3, it is clear that $R$ is $(S_2)$. Property $(R_1)$ is immediate. $\square$

There are also:

• 4 comment(s) on Section 10.157: Serre's criterion for normality

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).