Henselization is compatible with quotients.

Lemma 10.155.10. 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 10.155.9. $\square$

Comment #2805 by Minseon Shin on

Suggested slogan: Henselization is compatible with quotients.

There are also:

• 6 comment(s) on Section 10.155: Henselization and strict henselization

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).