RING WITH LEFT SMALL ANNIHILATOR CONDITIONS

Abstract

The study of Ring characteristics through Jacobson radical suggests new studies on the small annihilator ideals and its applications. Left small annihilator ideals of a ring has been W.K. Nicholson, Yiqiang Zhou presented in [3]. A right ideal A of the ring R is called a small ideal if for every right ideal B of R that A + B = R then B = R; A is called a left small annihilator ideals if l (B) = 0 (l (B) is a left annihilator of B). The purpose of this paper is to study the left small annihilator ideals that W.K. Nicholson and Yiqiang Zhou have contributed. Since then we would like to develop a number of ring characteristics, such as the Ikeda-Nakayama ring, the Artin ring, and the strong π-regular ring with small annihilator conditions.