Lemma 27.7.6. 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 27.7.5 because a Noetherian scheme has a Noetherian underlying topological space (Lemma 27.5.5 and Topology, Lemma 5.9.2. $\square$

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