(a) The following conditions on a field K are equivalent:

(i) every irreducible polynomial in K[x] is separable;

(ii) every algebraic closure K of K is Galois over K;

(iii) every algebraic extension field of K is separable over K;

(iv) either char K = 0 or char K = p and K = K^P. A field K that satisfies (i)-(iv) is said to be perfect. (b) Every finite field is perfect.