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Math Help - It's morphing time!

  1. #1
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    It's morphing time!

    Let R and S be rings and let f:R->S be a non-zero homomorphism.

    i) Show that if R=F is a field, then f is 1 to 1.
    ii) Is f 1 to 1 if R is an integral domain? Prove or give a counterexample.
    Thanks
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  2. #2
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    i) What is the kernel of a ring morphism, and what is such a thing in a field?

    ii) Do you know the characteristic?
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