Let Z be the ring of integers, and let R be a ring without identity. Let S = Z x R be the ring with addition and multiplication defined by (k, a) + (n, b) = (k + n, a + b) and (k, a)(n, b) = (kn, kb + na + ab), where k and n are in Z, and a and b are in R. Which of the following must be true about S? I. S is a ring with identity. II. S has a subring isomorphic to R. III. S is an integral domain (it has no zero- divisors). (A) I only (B) II only (C) I and II only (D) I and III only (E) I, II, and III 18

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