Which of the following is a ring with the usual operations of addition and multi

Question

Which of the following is a ring with the usual operations of addition and multiplication? For each structure that is not a ring, list the ring axioms that are not satis?ed. (a) N (natural numbers) (b) the closed interval [-1, 1] (c) {a + bi: a, b in Z}, where i^2 = -1 (Z refers to integers) (d) {bi: b in Z}, where i^2 = -1 The answer to part b is already solved, b) The interval [-1, 1] is not a ring because it is not closed under addition. (for example, 3/4 + 3/4 is not an element of [-1, 1]). 

Explanation / Answer

(b) the closed interval [-1, 1]

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