On the Structure of $T$-Closed Dual Rickart Modules

Authors

  • Mohamed Fadel Aidara Université Iba Der Thiam de Thiès
  • Papa Cheikhou Diop Université Iba Der Thiam de Thiès
  • Mamadou Barry Université Cheikh Anta Diop de Dakar

DOI:

https://doi.org/10.29020/nybg.ejpam.v19i2.7551

Keywords:

$T$-essential submodules, $T$-closed submodules, $T$-closed dual Rickart modules

Abstract

We introduce and study the notion of T-closed dual Rickart modules, which generalizes that of closed dual Rickart modules. A right R-module M is called T-closed dual Rickart if for every endomorphism f of M, the image im(f) is a T-closed submodule of M, where T is a fixed submodule of M. We establish fundamental properties of this class, including its behavior under direct summands, direct sums, and homomorphic images. Characterizations in terms of the endomorphism ring and several equivalent conditions are provided. We also explore connections with well-known classes of modules such as coquasi-Dedekind, continuous, and quasi-continuous modules. Examples are provided to illustrate and delimit the theory.

Author Biography

  • Papa Cheikhou Diop, Université Iba Der Thiam de Thiès

    Departement de Mathématiques, Université Iba Der Thiam de Thiès

References

Published

2026-07-28

Issue

Vol. 19 No. 2: (April 2026)

Section

Algebra

License

Copyright (c) 2026 Mohamed Fadel Aidara, Papa Cheikhou Diop, Mamadou Barry

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

On the Structure of $T$-Closed Dual Rickart Modules. (2026). European Journal of Pure and Applied Mathematics, 19(2), 7551. https://doi.org/10.29020/nybg.ejpam.v19i2.7551