Definition:Perfect Field

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Definition

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 $F$


Also see

  • Results about perfect fields can be found here.


Examples