Lemma 10.156.2 (05WQ)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.156: Henselization and quasi-finite ring maps
Lemma 10.156.2 (cite)

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Henselization is compatible with quotients.

Lemma 10.156.2. Let $R$ be a local ring with henselization $R^ h$. Let $I \subset \mathfrak m_ R$. Then $R^ h/IR^ h$ is the henselization of $R/I$.

Proof. This is a special case of Lemma 10.156.1. $\square$

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Comment #2805 by Minseon Shin on September 13, 2017 at 21:04

Suggested slogan: Henselization is compatible with quotients.

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