Pure Essential-Coessential and Pure Essential-Coclosed Submodules

Authors

  • Omar Hameed Ibrahim Department of Mathematics, University of Baghdad, College of Science. Baghdad, Iraq.
  • Nuhad Salim Al-Mothafar Department of Mathematics, University of Baghdad, College of Science. Baghdad, Iraq.

DOI:

https://doi.org/10.29304/jqcsm.2025.17.11985

Keywords:

pure submodules, pure essential submodules, coessential submodules, coclosed submodules

Abstract

During this work, we introduce concepts named pure-essential coessential sub-modules and pure- essential coclosed submodules. Various properties related with these concepts are considered. Let ,  be sub-modules of an -module  in which case , subsequently   is called pure essential-coessential sub-module of , if   , and  is said to be pure essential-coclosed sub-module, if   implies that .

Downloads

References

F. Kasch, Modules and Rings. 1982. doi: 10.1017/cbo9780511529962.

A. S. Mijbass and N. K. Abdullah, “Semi-essential submodules and semi-uniform modules,” Kirkuk J. Sci., vol. 4, no. 1, pp. 48–58, 2009.

M. A. Ahmed and M. R. Abbas, “On semi-essential submodules’’, Ibn Al-Haitham, J. for Pure & Applied Science, Vol. 28 (1), pp:179- 185, 2015

F. W. Anderson and K. R. Fuller, “Rings and Categories of Modules”, Springer-Verlage, New York, 1992.

O. H. Ibrahim, and N. S. Al-Mothafar, “Pure Essential Submodules”, Iraqi J. Sci. (Accepted), 2024.

Ganesan, L. and Vanaja, N. “Modules for which every submodule has a unique coclosure”. Comm. Algebra, vol.30, no.5, pp. 2355-2377, 2002.

Firas Sh. F and Sahira M. Y. “ET-Coessential and ET-Coclosed submodules”, Iraqi J. Sci., vol.60, no.12, pp. 2706-2710, 2019.

A. A. Abduljaleel and S. M. Yaseen, “Large-Coessential and Large-Coclosed submodules’’, Iraqi J. Sci., pp. 4065-40670, 2021.

A. Kabban and W. Khalid, “On Jacobson-small submodules,” Iraqi J. Sci., vol. 60, no. 7, pp. 1584–1591, 2019.

H. R. Baanoon and W. Khalid, “e∗-Essential Small Submodules and e∗-Hollow Modules,” Eur. J. Pure Appl. Math., vol. 15, no. 2, pp. 478–485, 2022, doi: 10.29020/nybg.ejpam.v15i2.4301.

C. Nebiyev and H. H. Ökten, “r-Small Submodules,” vol. 3, no. 1, pp. 33–36, 2020.

I. M. A. Hadi and S. H. Aidi, “On e-small submodules,” Ibn AL-Haitham J. Pure Appl. Sci., vol. 28, no. 3, pp. 214–222, 2017.

O. H. Ibrahim, and N. S. Al-Mothafar, “Pure Essential Small Submodules and Pure Essential Hollow Modules”, AIP conference proceedings, ISSN; 0094-243X, 1551-7616, (Accepted), 2024.

Downloads

Published

2025-03-30

How to Cite

Hameed Ibrahim, O., & Salim Al-Mothafar , N. (2025). Pure Essential-Coessential and Pure Essential-Coclosed Submodules. Journal of Al-Qadisiyah for Computer Science and Mathematics, 17(1), Math. 9–15. https://doi.org/10.29304/jqcsm.2025.17.11985

Issue

Section

Math Articles