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Prove F is a field where F maps to itself

  1. Nov 27, 2008 #1
    Hello, I am not exactly sure how to go about proving a a Field with given properties is a field.
    Any help would be appreciated. At least a push in the right direction/

    1. The problem statement, all variables and given/known data
    [​IMG]


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 27, 2008 #2

    Office_Shredder

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    Probably by showing it satisfies the field axioms...

    it's tough to be more specific without knowing what properties you're talking about
     
  4. Nov 27, 2008 #3
    Here is the problem

    [​IMG]
     
  5. Nov 27, 2008 #4

    HallsofIvy

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    First you say F "maps to itself" which makes no sense. Then you say "prove that a field is a field"!

    In fact, the problem you posted says neither of those. It says:

    If [itex]\phi[/itex] is an isomorphism from a field F to itself, and [itex]F_\phi[/itex] is defined as {x| [itex]\phi(x)= x[/itex]}, in other words, the set of all member of F that [itex]\phi[/itex] does not change, prove that [itex]F_\phi[/itex] is a field.

    Office Shredder told you how to do that: what are the "axioms" or requirements for a field?
     
  6. Nov 27, 2008 #5
    Obviously I did not understand the problem in its entirety . I believe I understand it now, and thanks to your assistance.
     
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