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

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Advance Math

A ?eld F is said to be perfect if every polynomialover F is separable. Equivalently,
every algebraic extension of F is separable. Thus ?elds ofcharacteristic zero and
?nite ?elds 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 elementof F. For short we
write F = F p.

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