Exercise 1. Let R and S be rings with identity, p: R → S a homomorphism of rings with p(1r) = 1s, s e S and f e R[x]. Compute p,(f) if (a) R=Z,S = Z, p(n) = [n]5 for all ne Z, s = [2]; and f = r³ + 2x + 1. (b) R= R, S = C, p(r) = r for all r e R, s = i and ƒ = r³ + 2x² + x +2. (c) R = C, S = C[x], p(a+bi) = a – bi for all a, b e R, s =r and f = ix³ – xª + (2 – i)x³ + x² – ix + (3 + 2i).

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