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Fields- strange problem

  1. Mar 28, 2005 #1
    Let K=Q(i,(1+i)^(1/3)).
    Describe all of K's embeddings in C.
    (C-Complex Field, Q-Rational Field).

    Describe? Could it be the answer is just the identity? How could I prove that?

    Thanks in advance! :smile:
     
  2. jcsd
  3. Mar 28, 2005 #2

    matt grime

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    i must go to some element that squares to 1, and 1 must go to 1, so how many choices can that be?
     
  4. Mar 28, 2005 #3
    Good point, stupid me.
    (You meant -1 I suppose).

    So actually, it is true that for Q, the only embedding is id?
    (1 must go to 1, therefore N - Natural numbers - must go to N, and therefore Q must go to Q)

    And in this case, I have like... 6 choices or so? (i goes to i or -i, plus playing with the cubic root a little bit)

    I'm gonna go try and formalize it. I'll come back if I have any prob.
    Thanks a lot!

    Oh, and if I wrote sth. stupid, feel free to throw it in my face. :biggrin:
     
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