Perfect Field

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

$F^p={x^p|x in F}=F.$

See also

Extension Field, Field, Galois Theory, Purely Inseparable Extension, Separable Extension

This entry contributed by Todd Rowland

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Rowland, Todd. "Perfect Field." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/PerfectField.html

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