• Thaar Younis Ghawi Department of Mathematics, College of Education, University of Al-Qadisiyah, Iraq
• Narjis Mujtabah Kamil Al-Samawah Education Directorate, Iraqi Ministry of Education, Iraq
Keywords: g-small submodules, principally ⨁-g-supplemented modules, principally sgrs^⊕-modules, ⨁-PG-Rad_g-supplemented modules

### Abstract

In this paper, a new concept has been presented that is a stronger than a previous concept called -G--supplemented. The basic definition is in an  ring where an -module  is said to be principally -G--supplemented (shortly, -PG--supplemented) if any cyclic submodule  of  with , there exists a direct summand  of  such that  and . A set of properties and relations between previous modules and the given module has been dealt with simple examples illustrating those relations.

### References

[1] M. Alkan and A. Harmanci, On summand sum and summand intersection property of modules, Turk. J. Math., 26(2002), P. 131-147.
[2] E. Büyükaşik and Y. Demirci, Weakly distributive modules. Applications to supplement submodules, Proc. Indian Acad. Sci., 120(2010), P. 525-534.
[3] T. Y. Ghawi, On a class of g-lifting modules, J. of Discrete Mathematical Sciences & Cryptography, 24 (6) (2021), P. 1857-1872.
[4] K. R. Goodearl, Ring theory, Nonsingular rings and modules, Dekker, Newyork, 1976.
[5] N. M. Kamil and T. Y. Ghawi, Strongly generalized ⨁-radical supplemented modules, Journal of Discrete Mathematical Sciences & Cryptography, 2022, to appear.
[6] N. M. Kamil and T. Y. Ghawi, Principally strongly generalized ⨁-radical supplemented modules, Journal of Al-Qadisiyah for Computer Science and Mathematics, 14(2022) (1), P. 34-.
[7] F. Kasch, Modules and rings module, Academic press, London, 1982.
[8] W. Khalid and A. Amer, Generalized radical g-supplemented modules, International Journal of Science and Research, 6(10) (2017), P. 1383-1385.
[9] B. Kosar, C. Nebiyev and N. Sokmez, G-supplemented modules, Ukrainian mathematical journal 67(6) (2015), P. 861-864.
[10] M. M. Obaid and T. Y. Ghawi, Principally g-supplemented modules, 9th International Scientific Conference of Iraqi Al-Khwarizmi Society, 2022, to appear.
[11] M. M. Obaid and T. Y. Ghawi, Principally ⨁-g-supplemented modules, Journal of Al-Qadisiyah for Computer Science and Mathematics, 14(2022) (1), P. 24-33.
[12] A. C. Özcan, A. Harmanci and Smith P. F., Duo modules, Glasgow Math. J., 48(3) (2006), P. 533-545.
[13] T. C. Quynh, and Tin P. H., Some properties of e-supplemented and e-lifting modules, Vietnam J. Math., 41(3) (2013), P. 303-312.
[14] R. Wisbauer, Foundations of module and ring theory, Gordon and Breach, Reading, 1991.
[15] D. X. Zhou and X. R. Zhang, small-essential submodule and morita duality, south-east Asian Bull. Math., 35(2011), P. 1051-1062.
Published
2022-09-24
How to Cite
Ghawi, T., & Kamil, N. (2022). Principally ⨁-G-〖Rad〗_g-supplemented modules. Journal of Al-Qadisiyah for Computer Science and Mathematics, 14(3), Math Page 75-79. https://doi.org/10.29304/jqcm.2022.14.3.1029
Issue
Section
Math Articles