Field Theory - Algebraic Extensions - D&F - Section 13.2 - Exercise 7, page 530

Exercise 7 in Section 13.2 Algebraic Extensions, page 530 of Dummit and Foote states the following:

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7. Prove that .

Conclude that .

Find an irreducible polynomial satisfied by

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I am somewhat overwhelmed by this problem ... can someone advise me on an approach ... and, indeed, get me started?

Peter

Re: Field Theory - Algebraic Extensions - D&F - Section 13.2 - Exercise 7, page 530

Let

These equations show that

Re: Field Theory - Algebraic Extensions - D&F - Section 13.2 - Exercise 7, page 530

For the irreducible polynomial, take powers.

From those, you should be able to find a relationship such that if , then . Hint: the problem tells you you don't need to go past .