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Field extension

  • Thread starter johnson123
  • Start date
  • #1
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Homework Statement



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:

Answers and Replies

  • #2
morphism
Science Advisor
Homework Helper
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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:

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