Prove or give a counterexample: for any two rings R and S, neither equal to {0},

the direct product RxS contains 0-divisors.

I have no idea where to start.

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- Apr 19th 2013, 07:42 PMchristianwosRings and zero-divisors problem
Prove or give a counterexample: for any two rings R and S, neither equal to {0},

the direct product RxS contains 0-divisors.

I have no idea where to start. - Apr 19th 2013, 09:38 PMGusbobRe: Rings and zero-divisors problem
Hint (in fact this is practically a solution): $\displaystyle (1,0)\cdot (0,1) = (0,0)$

- Apr 20th 2013, 06:45 PMchristianwosRe: Rings and zero-divisors problem
Thank you!