The Stacks project

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. $\square$

Comments (1)

Comment #2805 by Minseon Shin on

Suggested slogan: Henselization is compatible with quotients.

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View Lemma 10.156.2 as pdf