TARU PUBLICATIONS
Journal of Discrete Mathematical Sciences and Cryptography cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

Purely co-closed and purely co-essential sub-modules

* ,

* Corresponding author · click or hover a name for details

pp. 1137–1144Vol. 28Issue 4-AJune 2025DOI: 10.47974/JDMSC-2119 Crossmark XML
Received:
10 Dec 2024
Published Online:
26 Jun 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2119
Pages:
1137–1144

Abstract

In this article, the idea for this study is to present two concepts co-closed and purely co-essential sub-modules-that generalize co-closed and co-essential sub-modules. We study the relationship between purely co-closed and purely co-essential sub-modules by adding some of the properties of co-closed and co-essential sub-modules to them.

Keywords

Subject Classifications

22E45

References

[1] K. Ahmmed and N. S. Mothafar, “Pr-small R-sub-modules of modules and Pr-radicals,” Journal of Interdisciplinary Mathematics, vol. 26, no. 7, pp. 1511–1516 (2023).
[2] A. G. Nauom and B. H. Al-Bahranny, “Modules with Pure Sum Property, Iraqi,” Journal of Science, vol. 43, no. 3 (2002).
[3] A. A. Ahmed, I. A. Dhari, and Z. Atiya, “Purely Small and Purely Hollow Modules,” Iraqi Journal of Science, vol. 63, no. 12, pp. 5487–5495 (2022).
[4] K. Goodearl, Ring theory, nonsingular rings and modules. New York: Marcel Dekker (1976).
[5] K. Ahmad and N. Al-Mothafar, “Pure-Hollow Modules and Pure-Lifting Modules,” Iraqi Journal of Science, vol. 65, no. 3, pp. 1571–1577 (2024).
[6] M. K. Abbas, Y. Talebi, I. A. Hadi, and Z.-E. Submodules, “Z-Essential Submodules,” Iraqi Journal of Science, vol. 65, no. 3, pp. 1521–1530 (2024).
[7] I. H. Muslem, Some Types of Retractable and Compressible Modules, M.Sc. thesis (2016).
[8] H. Hamdi and N. Al-Mothafar, “On-Purely-Small Sub-modules,” Journal of Interdisciplinary Mathematics (2024).
[9] Z. A. Elbast and P. F. Smith, “Multiplication Modules,” Comm. In Algebra, vol. 10, no. 4, pp. 755–779 (1988).
[10]     R. H. Baanoon, I_(F^* ) - Lifting Modules For Image Of Fully Invariant Sub-modules (2023).
[11] F. Kasch, Modules and Rings. London: Academic Press (1982).
[12] I. S. Ahmed, A. Al-fayadh, H. H. Ebrahim, and L. S. Abdalbaqi, “Implementation of the Neutrosophic Sets in Measurable Space with Respect to Neutrosophic Ring,” Int. J. Neutrosophic Sci., vol. 25, no. 3, pp. 187–193 (2025).
[13] A. S. Mohammed, I. S. Ahmed, and S. H. Asaad, “Study of the rings in which each element express as the sum of an idempotent and pure,” Int. J. Nonlinear Anal. Appl., vol. 12, no. 2, pp. 1719–1724 (2021), doi: 10.22075/IJNAA.2021.5311.

Views: 90Downloads: 6Citations: 0