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Math Help - Extension Field

  1. #1
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    Extension Field

    1.Let F be an extension field of K and let u be in F. Show that K(a^2)contained in K(a) and [K(u):K(a^2)]=1 or 2.

    2.Let F be an extension field of K and let a be in F be algebraic over K with minimal polynomial m(x). Show that if degm(x) is odd then K(u)=K(a^2).



    Ideas:
    1.I was thinking of looking at [K(u):K(a)][K(a):K(a^2)]

    2.Well I know if a, is algebraic, then there exists a minimal polynomial m(x) such that m(a)=0. The degrees is what confuses me
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  2. #2
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    These two I am getting nowhere with. Am I on the right track or is there a better direction to go?
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  3. #3
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    2. I was thinking of somehow using a theorem stating [F:K]=[F:K(u)][K(u):K]
    based on the deg m(x) being odd, I would say deg m(x)=2n+1
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  4. #4
    Senior Member Shanks's Avatar
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    What is u in problem one?
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