Key Words: Fields, Galois Theory, Spitting Fields, Algebraic Closure, Normality
Problem: (4) If F is a spitting field over K of S, then F is also a spitting field
over K of the set T of all irreducible factors of polynomials in S.
(5) If f in K[x] has degree n, F is a spitting field of f over K, then [F:K] divides n!. Solution step by step: Click to download printable solution