Lemma 10.144.2. Let $R \to R[x]_ g/(f)$ be standard étale.

The ring map $R \to R[x]_ g/(f)$ is étale.

For any ring map $R \to R'$ the base change $R' \to R'[x]_ g/(f)$ of the standard étale ring map $R \to R[x]_ g/(f)$ is standard étale.

Any principal localization of $R[x]_ g/(f)$ is standard étale over $R$.

A composition of standard étale maps is

**not**standard étale in general.

## Comments (2)

Comment #4606 by Rex on

Comment #4776 by Johan on