Let f be a homomorphism of a ring R onto a ring R'. Prove that (i) if I is an ideal of R, then f(I) is an ideal of R'; (ii) if I' is an ideal of R', then f-¹(I') is an ideal of R and f−¹(I') 2 Ker f; (iii) if R is commutative and I and J are two ideals of R, then ƒ(I+J) = f(I) + f(J) and f(IJ) = f(I)f(J).

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