Lemma 10.151.2 (00UU)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.151: Unramified ring maps
Lemma 10.151.2 (cite)

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Lemma 10.151.2. Let $R \to S$ be a ring map. The following are equivalent

$R \to S$ is formally unramified and of finite type, and
$R \to S$ is unramified.

Moreover, also the following are equivalent

$R \to S$ is formally unramified and of finite presentation, and
$R \to S$ is G-unramified.

Proof. Follows from Lemma 10.148.2 and the definitions. $\square$

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