# Prove F is a field where F maps to itself

1. Nov 27, 2008

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

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 3, 2017
2. Nov 27, 2008

### Office_Shredder

Staff Emeritus
Probably by showing it satisfies the field axioms...

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

3. Nov 27, 2008

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

### 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?

5. Nov 27, 2008