Fusible rings

A ring R is called left fusible if every nonzero elenient is the sum of a left zero-divisor and a non-left zero-divisor. It is shovvn that if R is a left fusible ring and sigma is a ring automorphism of R, then R[x; sigma] and R[[x, sigma]] are left fusible. It is proved that if R is a left fusible ring, then M-n(R) is a left fusilale ring. Examples of fusible rings are complemented rings, special almost clean rings, and commutative Jacobson sernisirnple clean rings. A ring R is called left unit fusible if every nonzero element of R can be vvritten as the sum of a unit and a left zero-divisor in R. Full rings of continuous functions are fusible. It is also shown that if 1 =e(1) + e(2) +... + e(n) in a ring R, vvhere the e(i) are orthogonal idempotents and each e(i)Re(i) is left unit fusible, then R is left unit fusible. Finally, e give some properties of fusible rings.