Dual strongly Rickart modules

Tamadher Arif; Saad Abdulkadhim Al-Saadi

doi:10.24297/jam.v11i1.1295

Authors

Tamadher Arif College of Science for woman, Baghdad University.
Saad Abdulkadhim Al-Saadi College of Science, Al- Mustansiriyah University

DOI:

https://doi.org/10.24297/jam.v11i1.1295

Keywords:

strongly Rickart rings, strongly Rickar, modules, Rickart modules, dual Rickart modules, strongly regular rings.

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.