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Field Extensions

  • Thread starter Firepanda
  • Start date
  • #26
Office_Shredder
Staff Emeritus
Science Advisor
Gold Member
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You're overcomplicating things. We already finished the proof.

[K(x):K]=[K(x):K(x2)][K(x2):K]

We know [K(x):K(x2)] has to be odd, because [K(x):K] is. But [K(x):K(x2)] cannot be more than 2 (because we found x is a root of a quadratic polynomial). So it's either 2 or 1, and can't be 2, so must be one. But a degree one extension means that the two fields are the same
 
  • #27
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0
Oh sorry, I'll put it down to my lack of understanding of this topic so far, didn't really know where I was in the proof. That or it is because it's 5am ;)

Thanks you were a great help
 

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