Question: Now take R = S = Z. Can you find pairs of nonzero elements a and b in the ring T = Z Z

Now take R = S = Z. Can you find pairs of

Now take R = S = Z. Can you find pairs of nonzero elements a and b in the ring T = Z Z such that a b = 0? (Note that Z itself does not contain pairs of such elements.) If R and S are arbitrary rings, can you find a pair of nonzero elements a and b in T = Rx S such that a b = 0?

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