Definition 10.144.1. Let $R$ be a ring. Let $g , f \in R[x]$. Assume that $f$ is monic and the derivative $f'$ is invertible in the localization $R[x]_ g/(f)$. In this case the ring map $R \to R[x]_ g/(f)$ is said to be standard étale.

Comment #8133 by Oren Ben-Bassat on

Do we allow also $f=0$?.

Comment #8134 by Oren Ben-Bassat on

Oops please ignore that, I meant $R \to R_g$

Comment #8230 by on

Yes, because $R \to R_g$ is isomorphic to $R \to R_g[x]/(x) = R[x]_g/(x)$.

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).