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Field extension

  1. Feb 9, 2008 #1
    1. The problem statement, all variables and given/known data

    If a and b are algebraic over F of degree m and n, both relatively prime, then

    F(a,b)=mn, (i.e. [F(a,b):F]=mn)

    any comments are helpfull.
    Last edited: Feb 9, 2008
  2. jcsd
  3. Feb 9, 2008 #2


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    Science Advisor
    Homework Helper

    Your post is very incomplete. Are a and b algebraic over a field F? And by "F(a,b)=mn" do you mean "[F(a,b):F]=mn"?

    In which case, that m and n are relatively prime is important. Are you trying to say that [F(a,b):F]=[F(a):F][F(b):F]? This is false in general (why?).
    Last edited: Feb 9, 2008
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