Proof that Let F be a splitting field of K[x]. Without using Theorem 3.14 show

Proof that Let F be a splitting field of ∫ ϵ K[x]. Without using Theorem 3.14 show that F is normal over K.

Data from theorem 3.14

lf F is an algebraic extension field of K, then the following statements are equivalent.

(i) F is normal over K;

(ii) F is a splitting field over K of some set of polynomials in K[x];

(iii) if K̅ is an}'__ algebraic closure of K containing F, then for any K-monomorphism of fields σ: F → K, Im σ = F so that u is actually a K-auromorphism of F.