VÀNH VỚI CÁC ĐIỀU KIỆN CỦA LINH HÓA TỬ TRÁI MỊN

Abstract

The study o f Ring characteristics through Jacobson radical suggests new studies on the small annihilator ideals and its applications. Left small annihilator ideals o f a ring has been W.K. Nicholson, Yiqiang Zhou presented in [3]. A right ideal A o f the ring R is called a small ideal if for every right ideal B o f R that A + B = R then B = R; A is called a left small annihilator ideals if I (B) = 0 (I (B) is a left annihilator o f B).
The purpose o f 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 o f ring characteristics, such as the Ikeda-Nakayama ring, the Artin ring, and the strong 71-regular ring with small annihilator conditions.
Keywords: Small right Ideal, annihilator, jacobson radical.