A perfect field is a field such that every algebraic
extension is separable. Any field
in field characteristic zero, such as the
rationals or the p-adics,
or any finite field is a perfect field. More generally,
suppose the characteristic exponent
of the field
is
.
Then
is perfect iff
Perfect Field
See also
Extension Field, Field, Galois Theory, Perfect Closure, Purely Inseparable Extension, Separable ExtensionThis entry contributed by Todd Rowland
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Cite this as:
Weisstein, Eric W., with contributions by Todd Rowland. "Perfect Field." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PerfectField.html