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Simple question about extension fields?

  1. Nov 23, 2008 #1
    My notes say:
    If K is an extension of F then A={a in K | a is algebraic} is a subfield of K contained in F.

    But the elements in A need not be in F, right? Shouldn't it be:

    If K is an extension of F then A={a in K | a is algebraic} is a subfield of K contained in K.

    But I don't see the point of saying that-- if it's a subfield, of course it's in K. Also, I thought that AUF = K ... but that only happens when it is an algebraic extension... right?
     
  2. jcsd
  3. Nov 23, 2008 #2

    Hurkyl

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    I fixed a probably typo. And I assume you meant "a is algebraic over F"?
     
  4. Nov 23, 2008 #3
    A={a in K | a is algebraic over F}

    Like this, yes.
     
  5. Nov 23, 2008 #4
    never mind--- I get it now!

    Thanks again!
     
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