Lemma 10.165.3 (06DE)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.165: Geometrically normal algebras
Lemma 10.165.3 (cite)

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Localization preserves geometric normality.

Lemma 10.165.3. Let $k$ be a field. A localization of a geometrically normal $k$-algebra is geometrically normal.

Proof. This is clear as being a normal ring is checked at the localizations at prime ideals. $\square$

Comments (1)

Comment #3019 by Brian Lawrence on December 13, 2017 at 02:49

Suggested slogan: A localization of a geometrically normal algebra over a field is geometrically normal.

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