Lemma 27.7.7. Let $X$ be a locally Noetherian scheme. The following are equivalent:

1. $X$ is normal, and

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

Proof. Omitted. Hint: This is purely topological from Lemma 27.7.6. $\square$

Comment #276 by BB on

Maybe I'm missing some definition, but probably "normal" should not be an assumption on the locally noetherian scheme X in the statement.

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• 2 comment(s) on Section 27.7: Normal schemes

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