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Math Help - Field Theory - General Qiestion

  1. #1
    Super Member Bernhard's Avatar
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    Field Theory - General Qiestion

    I am studying field theory.

    A general question I have is the following:

    Let  E \supseteq F be fields and let  u \in E .

    Now, if I determine an irreducible polynomial in F[x] such that f(u) = 0 in E, can I conclude that I have found the minimal polynomial of u over F.

    Can someone please help?

    Peter
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  2. #2
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    Re: Field Theory - General Qiestion

    No because the minimal polynomial is monic. You may have a constant multiple of the minimal polynomial. If you have an irreducible monic polynomial in F[x] such that f(u) = 0 in E, then you can conclude you have found the minimal polynomial of u over F.
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  3. #3
    Super Member Bernhard's Avatar
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    Re: Field Theory - General Qiestion

    Yes, you are right of course ... Thanks!!!

    Peter
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