Key Words: Fields, Galois Theory, Spitting Fields, Algebraic Closure, Normality
Problem: (11) If F is generated by a (possibly infinite) set of separable elements over K, then
F is a separable extension of K.
(12) Let E be an intermediate field of the extension F:K.
(a) If u in F is separable over K, then u is separable over E ;
(b) If F is separable over K, then F is separable over E and E is separable over K.
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