Abstract: The authors  introduce the concepts of left (right) zero-divisor rings,a class of rings without identity.A ring R is called left (right) zero-divisor if rR(a)≠0(lR(a)≠0) for every a∈R.The authors  investigate the relations between left (right) zero-divisor rings and related rings,and give equivalent characterizations of left zero-divisor rings.

Key words: zero-divisor, left zero-divisor ring, reversible ring, symmetric ring, semicommutative ring, p.p.-ring, Armendariz ring