# Rings and zero-divisors problem

• April 19th 2013, 07:42 PM
christianwos
Rings 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.
• April 19th 2013, 09:38 PM
Gusbob
Re: Rings and zero-divisors problem
Hint (in fact this is practically a solution): $(1,0)\cdot (0,1) = (0,0)$
• April 20th 2013, 06:45 PM
christianwos
Re: Rings and zero-divisors problem
Thank you!