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).

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A First Course In Abstract Algebra

ISBN: 9780201763904

7th Edition

Authors: John Fraleigh

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Question Posted: Jan 16, 2023 02:50 AM

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Let K be a finite normal extension of F. a. For a K, show that is

Question:

f(x) = Π (-σ(α)) σεG(K/F)

Step by Step Answer:

a For GKF we have a natural extension of to an automorphism of Kx where 0 1 x n x ...View the full answer

A First Course In Abstract Algebra

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