Dual strongly Rickart modules

Abstract

In this paper we introduce and study the concept of dual strongly Rickart modules as a stronger than of dual Rickart modules [8] and a dual concept of strongly Rickart modules. A module M is said to be dual strongly Rickart if the image of each single element in S = End R (M) is generated by a left semicentral idempotent in S. If M is a dual strongly Rickart module, then every direct summand of M is a dual strongly Rickart. We give a counter example to show that direct sum of dual strongly Rickart module not necessary dual strongly Rickart. A ring R is dual strongly Rickart if and only if R is a strongly regular ring. The endomorphism ring of d-strongly Rickart module is strongly Rickart. Every d-strongly Rickart ring is strongly Rickart. Properties, results, characterizations are studied.