On π-endo.Rickart modules

Abstract

This paper examines the concept of pi-e.Rickart modules, which can be viewed as analogous to the pi-Rickart property observed in rings. This examination is conducted within the field of module theory, utilizing the endomorphism ring as a framework. It is demonstrated that p-e.Rickart modules lie between p-e.Baer and endo-p.q.-Baer modules. Several module theoretical properties are investigated and the ring of endomorphisms of these modules are studied. Moreover, we explore the p-e.Rickart property of M[X]R[X] and M [[ x ]] R [[ x ; a ]] . Illustrative examples are given to clarify and specify the scope of the results.