Insights into dual Rickart modules: Unveiling the role of second cosingular submodules

Authors

  • M. Khudhair Abbas Technical College of Management, Baghdad Middle Technical University Baghdad, Iraq.
  • Y. Talebi Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
  • I. Mohammed Ali Department of Mathematics, College of Education on Ibn-Al-Haithm, University of Baghdad, Baghdad, Iraq

Keywords:

dual Rickart module, T-dual Rickart module, wT d-Rickart module, t-dual Baer module, weak T-dual Baer module

Abstract

In this paper, we propose a new type of module by focusing on the second cosingular submodule of a module. We define a module M as weak T-dual Rickart if, for any homomorphism φ ∈ EndR(M), the submodule φ(Z̄2(M)) lies above a direct summand of M. We prove that this property is inherited by direct summands of M. We also introduce weak T-dual Baer modules and provide a complete characterization of such modules where the second cosingular submodule is a direct summand. Furthermore, we present a characterization of (semi)perfect rings in which every (finitely generated) module is weak T-dual Rickart.

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Published

2024-12-31

How to Cite

Insights into dual Rickart modules: Unveiling the role of second cosingular submodules. (2024). Journal of Prime Research in Mathematics, 20(2), 117 – 124. https://jprm.sms.edu.pk/index.php/jprm/article/view/235