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.