Lemma 28.7.4 (033L)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 28: Properties of Schemes
Section 28.7: Normal schemes
Lemma 28.7.4 (cite)

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Lemma 28.7.4. Let $X$ be an integral scheme. Then $X$ is normal if and only if for every nonempty affine open $U \subset X$ the ring $\mathcal{O}_ X(U)$ is a normal domain.

Proof. This follows from Algebra, Lemma 10.37.10. $\square$

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