On fusible rings

Abstract

A ring R is called left fusible if every nonzero element is the sum of a left zero-divisor and a non-left zero-divisor, and R is called uniquely left fusible if for any there exists a unique left zero-divisor z such that a – z is non-left zero-divisor. We show that a left fusible ring R is uniquely left fusible if and only if either R is a domain or R has a unique non-left zero-divisor element.