2-absorbing $I$-prime and 2-absorbing $I$-second submodules

Document Type : Research Paper

Author

Department of Mathematics, Farhangian University, Tehran, Iran

Abstract

Let $R$ be a commutative ring and let $I$ be an ideal of $R$. In this paper, we will introduce the notions of 2-absorbing $I$-prime and 2-absorbing $I$-second submodules of an $R$-module $M$ as a generalization of 2-absorbing and strongly 2-absorbing second submodules of $M$ and explore some basic properties of these classes of modules.

Keywords

References

[1] D. F. Anderson, A. Badawi, On n-absorbing ideals of commutative rings, Comm. Algebra 39 (2011), 1646-1672.
[2] H. Ansari-Toroghy, F. Farshadifar, Some generalizations of second submodules, Palestine Journal of Mathematics, 8 (2) (2019), 159-168.
[3] H. Ansari-Toroghy, F. Farshadifar, S. Maleki-Roudposhti, n-absorbing and strongly n-absorbing second submodules, Bol. Soc. Paran. Mat., to appear.
[4] A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. 75 (2007), 417-429.
[5] A. Y. Darani, F. Soheilnia, 2-absorbing and weakly 2-absorbing submoduels, Thai J. Math. 9(3) (2011), 577-584.
[6] J. Dauns, Prime submodules, J. Reine Angew. Math. 298 (1978), 156-181.
[7] L. Fuchs, W. Heinzer, 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 (2006), 121-145.
[8] S. Moradi, A. Azizi, Weakly 2-absorbing submodules of modules, Turk. J. Math. 40 (2016), 350-364.
[9] Sh. Payrovi, S. Babaei, On 2-absorbing submodules, Algebra Collq., 19 (2012), 913-920.
[10] S. Yassemi, The dual notion of prime submodules, Arch. Math. (Brno) 37 (2001), 273-278.
Algebraic Structures and Their Applications
Volume 6, Issue 2
November 2019
Pages 47-55

Files

Share

How to cite

Statistics