1. The problem statement, all variables and given/known data Let R be a ring that contains at least two elements. Suppose for each nonzero a in R, there exists a unique b in R such that aba=a. Show that R has no divisors of 0. 2. Relevant equations 3. The attempt at a solution Let a*c=0 where a,c are not equal to 0. aba=a implies aba-a=0=nac where n is any integer which implies that a(ba-1-nc)=0 I am not seeing the contradiction.