Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
    http://www.upload.mn/view/q77nuboss6set86gbhfs.jpg [Broken]

    2. Relevant equations

    3. The attempt at a solution
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Nov 27, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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
    Last edited by a moderator: May 3, 2017
  5. Nov 27, 2008 #4


    User Avatar
    Science Advisor

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook