# Isomorphism proof

Show that a homomorphism from a field onto a ring with more than one element must be an isomorphism.

Recall The the function f is an isomorphism if and only if f is onto and Kernel ={ 0}.

Please explain step by step with reasons in every step.

https://brainmass.com/math/linear-transformation/isomorphism-proof-74843

#### Solution Preview

Proof: Let g: F->R is a homomorphism from the field F onto the ring R. At least we can find two different elements a,b in F, such that g(a) is different form g(b).

First, I claim that g ...

#### Solution Summary

This is a proof regarding homomorphisms and isomorphisms.

$2.19