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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 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.