On \(\pi\)-Endo.Rickart Modules

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 \(\pi\)-e.Rickart modules lie between \(\pi\)-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 \(\pi\)-e.Rickart property of \(M[X]_{R[X]}\) and \(M[[x]]_{R[[x;\alpha ]]}\). Illustrative examples are given to clarify and specify the scope of the results.