On π-Endo.Rickart Modules

Maleki Y., Moussavi A., KARA ŞEN Y.

Iranian Journal of Science, 2024 (Scopus) identifier

  • Publication Type: Article / Article
  • Publication Date: 2024
  • Doi Number: 10.1007/s40995-024-01736-3
  • Journal Name: Iranian Journal of Science
  • Journal Indexes: Scopus
  • Keywords: Baer modules, Endomorphism rings, Polynomial extensions, Rickart modules, π-e.Baer modules, π-Rickart ring
  • Bursa Uludag University Affiliated: Yes

Abstract

This paper examines the concept of π-e.Rickart modules, which can be viewed as analogous to the π-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 π-e.Rickart modules lie between π-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 π-e.Rickart property of M[X]R[X] and M[[x]]R[[x;α]]. Illustrative examples are given to clarify and specify the scope of the results.