I am having trouble with this problem. It would be great if someone can help.

I want to prove that where is the cyclotomic field of 5th roots of unity, and

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- May 7th 2009, 07:31 PMnamelessguyField extension
I am having trouble with this problem. It would be great if someone can help.

I want to prove that where is the cyclotomic field of 5th roots of unity, and - May 8th 2009, 10:55 AMNonCommAlg
first see that is a root of the polynomial which is irreducible over by Eisenstein criterion. thus since we'll be done if we prove that

now suppose then from we'll get: which after simplifying

gives us: thus: therefore is a root of we actually proved that the roots of are exactly

thus there exists such that - May 8th 2009, 03:43 PMnamelessguy
Thank you very much for your help, NonCommAlg. So I understand that you let . Then squaring this equation twice and manipulate to get the polynomial. It is also the minimal polynomial correct? But I don't understand the notation you use below. Does it mean degree of

since - May 8th 2009, 07:15 PMNonCommAlg