A perfect field is a field F 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 F is p. Then F is perfect iff F^p congruent {x^p|x element F} = F.

extension field | field | purely inseparable extension | separable extension