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    Modern algebra

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    I am stuck with this question.

    If phi : F -> R is a nonzero homomorphism from a field F to a ring R, show that phi is one-to-one (Hint: recall that for a ring homomorphism, phi is one-to-one if and only if Ker(phi)={0}. )

    Can you help with this?

    Many thanks in advance

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    We do not consider the trivial case: phi(a)=0 for any a in F. In this case, phi is not ...

    Solution Summary

    This solution is comprised of a detailed explanation to show that phi is one-to-one.