Ring homomorphism proof

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  Many thanks in advance Proof: We do not consider the trivial case: phi(a)=0 for any a in F. In this case, phi is not one-to-one and phi is also a ring homomorphism. For the nontrivial case, we know phi(1)<>0 ("<>" means "not equal to").

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  73977 Ring homomorphism (See attached file for full problem description) --- 1. Show that if is a ring homomorphism and A is an ideal of R Then need not be an ideal of S.