## Tag `0258`

Chapter 40: Étale Morphisms of Schemes > Section 40.11: Étale morphisms

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 ringsif 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
(please see Definition \ref{definition-unramified-rings}).
\end{definition}
```

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