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Let $F$ be a field.
$F$ is a perfect field if and only if $F$ has no inseparable extensions.
$F$ 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 $F$
- $\Char F$ denotes the characteristic of $F$
- $\Frob$ denotes the Frobenius endomorphism on $F$
- Equivalence of Definitions of Perfect Field
- Frobenius Endomorphism on Field is Injective
- Definition:Separably Closed Field, a field with no separable extensions
- Results about perfect fields can be found here.