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Isomorphism proof

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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.

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Solution Summary

This is a proof regarding homomorphisms and isomorphisms.

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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 ...

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