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

$X$ is normal, and

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

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

$X$ is normal, and

$X$ 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).
$\square$

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## Comments (2)

Comment #6814 by Rubén Muñoz--Bertrand on

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