How about the ring R=Z (the integers). Every element in the integers is a nonzero divisor and there is no way to get a multiplicative inverse, right? (since no fractions and no modulos and probably something else too)? Thus wouldn't any element of the integers be a nonzero element that we are looking for? Am I on the right track? -Josie
Yea, that's the same example I found. You were on the right track, but to put it more succinctly you can observe that Z is an integral domain, meaning if an element isn't a unity then it is a nonzero element.
--Jniederh 02:41, 11 March 2009 (UTC)
