# Category:Definitions/Perfect Fields

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This category contains definitions related to Perfect Fields.

Related results can be found in Category:Perfect Fields.

Let $F$ be a field.

### Definition 1

$F$ is a **perfect field ** if and only if $F$ has no inseparable extensions.

### Definition 2

$F$ is a **perfect field** if and only if one of the following holds:

- $\Char F = 0$
- $\Char F = p$ with $p$ prime and $\Frob$ is an automorphism of $F$

where:

- $\Char F$ denotes the characteristic of $F$
- $\Frob$ denotes the Frobenius endomorphism on $F$

## Pages in category "Definitions/Perfect Fields"

The following 3 pages are in this category, out of 3 total.