Let
These equations show that
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
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 .