Let K be a finite normal extension of F. a. For a K, show that is
Question:
Let K be a finite normal extension of F.
a. For a ∈ K, show that
is in F[x]
b. Referring to part (a), show that f(x) is a power of irr(α, F), and f(x) = irr(α, F) if and only if K = F(α).
Transcribed Image Text:
f(x) = Π (-σ(α)) σεG(K/F)
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a For GKF we have a natural extension of to an automorphism of Kx where 0 1 x n x ...View the full answer
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