Let K be a normal extension of F, and let K F() Let irr(, F) x n a n 1 x n 1 a 1 x a 0 Referring to Exercise 17, show that N k F () (1) n a 0 , Tr k F () a n1 ...

Let fx irr F Because K F is normal over F it is a spl ...

Let K be a normal extension of F, and let K = F(). Let irr(, F)=x n

Question:

Let K be a normal extension of F, and let K = F(α). Let
irr(α, F)=xⁿ+a_n-1x^n-1 +· · · + a₁x + a₀.

Referring to Exercise 17, show that

N_k/F(α) = (−1)ⁿa₀,

Tr_k/F(α) = -a_n−1.

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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 normal extension of F, and let K = F(). Let irr(, F)=x n

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A First Course In Abstract Algebra

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