The Stacks project

Lemma 28.7.6. Let $X$ be a Noetherian scheme. The following are equivalent:

  1. $X$ is normal, and

  2. $X$ is a finite disjoint union of normal integral schemes.

Proof. This is a special case of Lemma 28.7.5 because a Noetherian scheme has a Noetherian underlying topological space (Lemma 28.5.5 and Topology, Lemma 5.9.2). $\square$

Comments (2)

Comment #6814 by Rubén Muñoz--Bertrand on

Minor typo: missing closing parenthesis at the end of the proof.

There are also:

  • 3 comment(s) on Section 28.7: Normal schemes

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