Question: (a) If u 1 , ... , U n E Fare separable over. K, then K(u 1 , ... , un) is a separable extension

(a) If u1, ... , Un E Fare separable over. K, then K(u1, ... , un) is a separable extension of K. 

(b) If F is generated by a (possibly infinite) set of separable elements over K, then F is a separable extension of K.

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Proof a Let L Ku1 un Since each ui is separable over K we know that KuiK degmi for some irreducible ... View full answer

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