# The Stacks Project

## Tag 0258

Definition 40.11.1. Let $A$, $B$ be Noetherian local rings. A local homomorphism $f : A \to B$ is said to be a étale homomorphism of local rings if it is flat and an unramified homomorphism of local rings (please see Definition 40.3.1).

The code snippet corresponding to this tag is a part of the file etale.tex and is located in lines 1048–1055 (see updates for more information).

\begin{definition}
\label{definition-etale-ring}
Let $A$, $B$ be Noetherian local rings.
A local homomorphism $f : A \to B$ is said to be a
{\it \'etale homomorphism of local rings}
if it is flat and an unramified homomorphism of local rings
\end{definition}

Comment #3277 by Dario Weißmann on April 15, 2018 a 3:11 pm UTC

Typo: a etale -> an etale.

There are also 2 comments on Section 40.11: Étale Morphisms of Schemes.

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