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

This paper examines the concept of \(\pi\) $\pi$ -e.Rickart modules, which can be viewed as analogous to the \(\pi\) $\pi$ -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 \(\pi\) $\pi$ -e.Rickart modules lie between \(\pi\) $\pi$ -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 \(\pi\) $\pi$ -e.Rickart property of \(M[X]_{R[X]}\) $M{[X]}_{R[X]}$ and \(M[[x]]_{R[[x;\alpha ]]}\) $M{[[x]]}_{R[[x;\alpha ]]}$ . Illustrative examples are given to clarify and specify the scope of the results.