Nearly Quasi Primary-2-Absorbing Submodules
DOI:
https://doi.org/10.29304/jqcm.2022.14.3.1037Keywords:
2-Absorbing submodules., 2-Absorbing quasi primary submodules., Jacobson of modules., Radical of submodules., Multiplication modules and projective modules.Abstract
Let be a nonzero unital left -module and be a commutative ring with nonzero identity. As a generalization of 2-Absorbing submodules, we provide the idea of Nearly Quasi Primary-2-Absorbing submodules in this article. As a proper submodule of is called the Nearly Quasi Primary-2-Absorbing submodule of , if whenever for , , implies that either or or . Several properties, characterizations and examples concerning this new notion are given.
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References
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[15] Ahamed, A. A. On Submodules of Multiplication Modules, M.Sc. Thesis, University of Baghdad, 1992.
[16] Ali, M. M. , Idempotent and Nilpotent Submodules of Multiplication Modules, Comm. Algebra,( 36) (2008), 4620-4642.
[17] Nuha, H. H. The Radical of Modules, M. Sc. Thesis, University of Baghdad, 1996.
[18] Ali, S. M. On Cancellation Modules, M. Sc. Thesis, University of Baghdad, 1993.
[2] Haibat, K. M and Omar, A. Abdalla. Pseudo Primary-2-ABSORBING SUBMODULES and Some Related Concepts, Ibn Al-Haitham Journal for pure and applied mathematics, 32 (3) (2019), 129-139.
[3] Omar, A. Abdalla, Ali Sh. Ajeel and Haibat, K. Mohammedali. Nearly Primary-2-Absorbing submodules and Other Related Concepts, Ibn Al-Haitham Journal for pure and applied mathematics, 34 (1) (2021), 116-124.
[4] Innam, M. A and Abdulrahman, A. H. Semi- 2-Absorbing Submodules and Semi-2-absorbing Modules, international Journal of Advanced Scientific and Technical Research, RS Publication, 5 (3) (2015), 521-530.
[5] H. Mostafanasab, E. Yetkin, U. Tekir and A. Y. Darani. On 2-absorbing primary submodules of modules over commutative rings. An. Sti. U. Ovid. Co-mat. 24(1) (2015), 335–351.
[6] Darani, A.Y and Soheilniai. F. 2-Absorbing and Weakly 2-Absorbing Submodules, Tahi Journal. Math, (9) (2011), 577-584.
[7] Badawi, A. On 2-Absorbing Ideals of Commutative Rings, Bull. Austral. Math. Soc, (75) (2007), 417-429.
[8] Lu, C. P. Prime Submodules of Modules, Comm. Math, University Spatula, (33) (1981), 61-69.
[9] Lu, C. P. M-radical of Submodules, Math. Japan. 34 (2) (1989), 211-219.
[10] Tekir, U. , Koc, S. , Oral, K. H. and Shum, K. P. , On 2-Absorbing Quasi-primary Ideals in commutative Rings, Communication in Mathematics and statistics, 4(1)( (2016), 55-62.
[11] Kos, S. Uregen, R. N and Tekir, U. On 2-Absorbing Quasi-primary Submodules, Faculty of Science and Mathematics, 31(10) (2017), 2943-2950.
[12] El-Bast, Z.A. and Smith, P.F. Multiplication modules, Comm. In Algebra 16(4) (1988), 755–779.
[13] Kasch, F. Modules and Rings, London Math. Soc. Monographs, New York, Academic press, 1982.
[14] Smith, P. F. Some remarks of Multiplication Modules, Arch. Math. (50) (1986), 223-225.
[15] Ahamed, A. A. On Submodules of Multiplication Modules, M.Sc. Thesis, University of Baghdad, 1992.
[16] Ali, M. M. , Idempotent and Nilpotent Submodules of Multiplication Modules, Comm. Algebra,( 36) (2008), 4620-4642.
[17] Nuha, H. H. The Radical of Modules, M. Sc. Thesis, University of Baghdad, 1996.
[18] Ali, S. M. On Cancellation Modules, M. Sc. Thesis, University of Baghdad, 1993.
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Published
2022-09-29
How to Cite
Abdullah, O. A., Dahash, M. E., & Mohammadali, H. K. (2022). Nearly Quasi Primary-2-Absorbing Submodules. Journal of Al-Qadisiyah for Computer Science and Mathematics, 14(3), Math Page 59–64. https://doi.org/10.29304/jqcm.2022.14.3.1037
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Math Articles
