A ﬁeld F is said to be perfect if every polynomial over F is separable. Equivalently,...

A ﬁeld F is said to be perfect if every polynomial over F is separable. Equivalently,
every algebraic extension of F is separable. Thus ﬁelds of characteristic zero and
ﬁnite ﬁelds are perfect. Show that if F has prime characteristic p, then F is perfect
if and only if every element of F is the pth power of some element of F. For short we
write F = F p.

Expert Solution

Colby Messinger answered 2 years ago

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