Classical and strongly classical 2-absorbing second submodules

Year 2020, Volume: 69 Issue: 1, 123 - 136, 30.06.2020

Faranak Farshadifar , Habibollah Ansari-toroghy

https://doi.org/10.31801/cfsuasmas.550201

Cited By: 3

Abstract

‎In this paper‎, ‎we will introduce the concept of classical (resp‎. ‎strongly classical) 2-absorbing second submodules of modules over a commutative ring as a generalization of 2-absorbing (resp‎. ‎strongly 2-absorbing) second submodules and investigate some basic properties of these classes of modules‎.

Keywords

2-absorbing second submodule‎, ‎classical 2-absorbing second submodule‎

References

• Ansari-Toroghy, H. and Farshadifar, F., The dual notion of some generalizations of prime submodules, Comm. Algebra, 39 (2011), 2396-2416.
• Ansari-Toroghy, H. and Farshadifar, F., The dual notion of multiplication modules, Taiwanese J. Math. 11 (4) (2007), 1189--1201.
• Ansari-Toroghy, H. and Farshadifar, F., On the dual notion of prime submodules, Algebra Colloq. 19 (Spec 1)(2012), 1109-1116.
• Ansari-Toroghy, H. and Farshadifar, F., On the dual notion of prime radicals of submodules, Asian Eur. J. Math. 6 (2) (2013), 1350024 (11 pages).
• Ansari-Toroghy, H. and Farshadifar, F., Some generalizations of second submodules, Palestine Journal of Mathematics, 8(2) (2019), 1-10.
• Ansari-Toroghy, H., Farshadifar, F., and Pourmortazavi, S. S., On the P-interiors of submodules of Artinian modules, Hacettepe Journal of Mathematics and Statistics, 45(3) (2016), 675-682.
• Badawi, A., On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. 75 (2007), 417-429.
• Barnard, A., Multiplication modules, J. Algebra, 71 (1981), 174-178.
• Ceken, S., Alkan, M. and Smith, P.F., The dual notion of the prime radical of a module, J. Algebra, 392 (2013), 265-275.
• Darani, A. Y. and Soheilnia, F., 2-absorbing and weakly 2-absorbing submoduels, Thai J. Math. 9(3) (2011), 577-584.
• Dauns, J ., Prime submodules, J. Reine Angew. Math., 298 (1978), 156--181.
• Fuchs, L., Heinzer, W. and Olberding, B., Commutative ideal theory without finiteness conditions: Irreducibility in the quotient filed, in : Abelian Groups, Rings, Modules, and Homological Algebra, Lect. Notes in Pure Appl. Math. 249 (2006), 121--145.
• Kaplansky, I., Commutative rings, University of Chicago Press, 1978.
• Mostafanasab, H., Tekir, U. and Oral, K.H., Classical 2-absorbing submodules of modules over commutative rings, European Journal of Pure and Applied Mathematics, 8(3) (2015), 417-430.
• Payrovi, Sh. and Babaei, S., On 2-absorbing submodules, Algebra Collq. 19 (2012), 913-920.
• Quartararo, P. and Butts, H. S., Finite unions of ideals and modules, Proc. Amer. Math. Soc. 52 (1975), 91-96.
• Sharpe, D.W. and Vamos, P., Injective modules, Cambridge University Press, 1972.
• Yassemi, S., The dual notion of prime submodules, Arch. Math. (Brno) 37 (2001), 273--278.
• Yassemi, S., The dual notion of the cyclic modules, Kobe. J. Math. 15 (1998), 41--46.