Th Let h:R - Sbe a homomorphism of rings and define a function :R[X] - S[x]...

 

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Th Let h:R - Sbe a homomorphism of rings and define a function :R[X] - S[x] by the rule (ao + a,x +... + a,x") = h(ao) + h(a,)x = h(a2)x2 + . .. + h(a,)x". Prove that (a) is a homomorphism of rings. (b) h is injective if and only if h is injective. (c) is surjective if and only if h is surjective. (d) If R= S, then R[x] = S[x]. Th Let h:R - Sbe a homomorphism of rings and define a function :R[X] - S[x] by the rule (ao + a,x +... + a,x") = h(ao) + h(a,)x = h(a2)x2 + . .. + h(a,)x". Prove that (a) is a homomorphism of rings. (b) h is injective if and only if h is injective. (c) is surjective if and only if h is surjective. (d) If R= S, then R[x] = S[x].