Purely co-closed and purely co-essential sub-modules
*Halah Qahtan HamdiCorresponding authorhala.hamdi@sc.uobaghdad.edu.iqDepartment of Mathematics College of Science University of Baghdad Department of Mathematics College of Science University of Baghdad Baghdad, IraqView full profile → , Nuhad S. Al-Mothafarnuhad.salim@sc.uobaghdad.edu.iqDepartment of Mathematics College of Science University of Baghdad Baghdad, Baghdad, IraqView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 10 Dec 2024
- Published Online:
- 26 Jun 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2119
- Pages:
- 1137–1144
Abstract
Keywords
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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.




