Lemma 10.162.4 (032S)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.162: Nagata rings
Lemma 10.162.4 (cite)

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Lemma 10.162.4. If $R$ is universally Japanese then any algebra essentially of finite type over $R$ is universally Japanese.

Proof. The case of an algebra of finite type over $R$ is immediate from the definition. The general case follows on applying Lemma 10.161.3. $\square$

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