A New Generalization of s-Weakly Regular Rings

Right (resp. left) s-weakly regular rings was first introduced by V. Gupta in 1984. Now, in the present paper we introduce and study a new generalization of right (resp. left) s-weakly regular rings, which is called right (resp. left) gs- weakly regular rings as for each a ∈ R; there exists a positive integer n = n(a); depending on a such that a ∈ aRa sup n /sup R (resp. a ∈ Ra sup n /sup Ra). Moreover, giving several characterizations, properties, main results of it and related it with other types of modules such as at modules and GP-injective modules.