Prove F is a field where F maps to itself

[shabbado]

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/

Homework Statement

http://www.upload.mn/view/q77nuboss6set86gbhfs.jpg

Homework Equations

The Attempt at a Solution

 

[Office_Shredder]

Probably by showing it satisfies the field axioms...

it's tough to be more specific without knowing what properties you're talking about

 

[shabbado]

Here is the problem

http://img56.imageshack.us/img56/2010/q3fg6.th.jpg

 

[HallsofIvy]

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

Office Shredder told you how to do that: what are the "axioms" or requirements for a field?

 

[shabbado]

Obviously I did not understand the problem in its entirety . I believe I understand it now, and thanks to your assistance.