Strongly $\psi $-$2$-absorbing second submodules

Document Type : Research Paper

Authors

1 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

2 Department of Mathematics Education, Farhangian University, Tehran, Iran

Abstract

 ‎Let $R$ be a commutative ring with identity and $M$ be an $R$-module‎. ‎Let $\psi‎ : ‎S(M)\rightarrow S(M) \cup \{\emptyset \}$ be a function‎, ‎where $S(M)$ denotes the set of all submodules of $M$‎. ‎The main purpose of this paper is to introduce and investigate the notion of strongly $\psi $-2-absorbing second submodules of $M$ as a generalization of strongly 2-absorbing second and $\psi $-second submodules of $M$‎.

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References

1. D. D. Anderson and M. Bataineh, Generalizations of prime ideals. Comm. Algebra 36 (2008), 686-696.
2. H. Ansari-Toroghy and F. Farshadifar, The dual notion of some generalizations of prime submodules, Comm. Algebra, 39 (2011), 2396-2416.
3. H. Ansari-Toroghy and F. Farshadifar, Some generalizations of second submodules, Palestine Journal of Mathematics, (2) 8 (2019), 1-10.
4. H. Ansari-Toroghy and F. Farshadifar, Fully idempotent and coidempotent modules, Bull. Iranian Math. Soc. (4) 38 (2012), 987-1005.
5. H. Ansari-Toroghy, F. Farshadifar, and S. Maleki-Roudposhti, n-absorbing and strongly n-absorbing second submodules, Bol. Soc. Parana. Mat., (1) 39 (2021), 9-22.
6. A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. 75 (2007), 417-429.
7. J. Dauns, Prime modules, J. Reine Angew. Math. 298 (1978), 156-181.
8. F. Farshadifar and H. Ansari-Toroghy,  -second submodules of a module, Beitr. Algebra Geom., (3) 61 (2020), 571-578.
9. F. Farshadifar, Modules with Noetherian second spectrum, J. Algebra Relat. Topics, (1) 1 (2013), 19-30.
10. L. Fuchs, W. Heinzer, and B. Olberding, Commutative ideal theory without niteness conditions: Irreducibility in the quotient  led, in : Abelian Groups, Rings, Modules, and Homological Algebra, Lect. Notes Pure Appl. Math. 249,
121-145, (2006).
11. S. Yassemi, The dual notion of prime submodules, Arch. Math. (Brno) 37 (2001), 273-278.
12. N. Zamani,  $\phi $-prime submodules. Glasgow Math. J. 52 (2) (2010), 253-259.
Journal of Algebra and Related Topics
Volume 12, Issue 2
January 2025
Pages 17-23

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