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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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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