Semi-essentially prime modules

Al-Hakeem, Mohammed Baqer Hashim; Al-Mothafar, Nuhad S.

doi:10.47974/JDMSC-1631

Open Access Research Article

Semi-essentially prime modules

^*Mohammed Baqer Hashim Al-HakeemCorresponding authormbhmsc2015110@gmail.comDepartment of MathematicsCollege of ScienceBaghdad UniversityBaghdad, IraqView full profile → , Nuhad S. Al-Mothafarnuhad.salim@sc.uobaghdad.edu.iqDepartment of MathematicsCollege of ScienceBaghdad UniversityBaghdad, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 1725–1730Vol. 26Issue 6September 2023DOI: 10.47974/JDMSC-1631 Crossmark XML

Received:: 03 Mar 2022
Published Online:: 01 Jun 2023
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1631
Pages:: 1725–1730

Abstract

Let R be a commutative ring with 1 and M be a (left) unitary R – module. This essay gives generalizations for the notions prime module and some concepts related to it. We termed an R – module M as semi-essentially prime if annR (M) = annR (N) for every non-zero semi-essential submodules N of M. Given some of their advantages characterizations and examples, and we study the relation between these and some classes of modules.

Keywords

Prime module Semi-essentially compressible module Essentially compressible module Fully prime module Semi-uniform module

Subject Classifications

32C25ˍ16P70

References

[1] Muna, A. Ahmed, “Weak Essential Submodules”, University of Baghdad, Ibn Al-Haitham J. for Pure & Appl. Um-Salama Science Journal Vol. 6(1) (2009).
[2] Ali. S. Mijbass and Nada. K. Abdullah, Semi-Essentially Submodule and Semi-Uniform Modules. J. of Kirkuk University-Scientific studies; 4 (1), 48-58 (2009).
[3] Muna, A. Ahmed, “Some Results on Weak Essential Submodules”, University of Baghdad, Ibn Al-Haitham J. for Pure & Appl. Baghdad Science Journal Vol.13 (3) (2016).
[4] Haithab A.Shahad and Nuhad S.Al-Muthafar, “On essential-prime submodules” Journal of Discrete Mathematical Sciences and Cryptography, Dol:10.1080/09720529.2021.1968572
[5] Israa. H. Muslem, “Some types of Retractable and Compressible Modules’’M.Sc.thesis. College of Education for pure Science, University of Baghdad (2016).
[6] Mohammed B. H. Alhakeem and Nuhad S. Al-Mothafar, “Semi-Essentially Compressible Modules and Semi-Essentially Retractable Modules” Iraqi Journal of Science, Too appear.
[7] Muna, A. Ahmed and maysaa R. Abbas, “On Semi-Essentially Submodules”, University of Baghdad, Ibn Al-Haitham J. for Pure & Appl. Sci; Vol. 28 (1) (2015).
[8] Inaam Mohammed Ali and Tha’ar Younis Ghawi, “Essentially Prime Modules and Related Modules” Journal of Basrah Researches ((Sciences)) Volume 37. Number 4. C (2011).
[9] R. L. McCasland and P. F. Smith, “Prime Submodules of Noetherian Modules”, Rocky Mt. Math. 23, 1041-1062 (1993).
[10] Omar M Al-Ragab & Nuhad S. Al-Mothafar, Radical semiprime submodules, Journal of Discrete Mathematical Sciences and Cryptography, 24:7, 1895-1899 (2021), DOI: 10.1080/09720529.2021.1957180.

Views: 221Downloads: 71Citations: 0