Question

prove that K is a normal extension of F if and only if K is the splitting field of some polynomial over F​

Answer 1

Answer:

The Theoram 2.2 An extension K/k is normal if and only if it is the splitting field of a polynomial. Proof. ... But K is generated by the zeroes of f, so K is the splitting field of f over k. (⇐) Suppose K = k(α1,...,αn) is the splitting field of a degree n polynomial g ∈ k where α1,...,αn are the zeroes of g.