Supplement Rickart Modules

Abstract

This paper introduces a new generalization of Rickart modules, namely the Supplement-Rickart module. Let  be a module over a ring  with identity, and let  denotes the endomorphism ring of . The module  is called Supplement-Rickart if for all is a supplement sub-module of . Moreover, several remarks and examples are included, and various properties together with connections to other related notions are analyzed.