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RESEARCH ARTICLE
Generalized 2-absorbing and strongly generalized 2-absorbing second submodules
H. Ansari-Toroghya, F. Farshadifarb, S. Maleki-Roudposhtia a Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 41335-19141, Rasht, Iran
b Department of Mathematics, Farhangian University, Tehran, Iran
Abstract:
Let R be a commutative ring with identity. A proper submodule N of an R-module M is said to be a 2-absorbing submodule of M if whenever abm∈N for some a,b∈R and m∈M, then am∈N or bm∈N or ab∈(N:RM). In [3], the authors introduced two dual notion of 2-absorbing submodules (that is, 2-absorbing and strongly 2-absorbing second submodules) of M and investigated some properties of these classes of modules. In this paper, we will introduce the concepts of generalized 2-absorbing and strongly generalized 2-absorbing second submodules of modules over a commutative ring and obtain some related results.
Keywords:
second, generalized 2-absorbing second.
Received: 06.12.2017
Citation:
H. Ansari-Toroghy, F. Farshadifar, S. Maleki-Roudposhti, “Generalized 2-absorbing and strongly generalized 2-absorbing second submodules”, Algebra Discrete Math., 29:2 (2020), 161–172
Linking options:
https://www.mathnet.ru/eng/adm749 https://www.mathnet.ru/eng/adm/v29/i2/p161
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Abstract page: | 83 | Full-text PDF : | 61 | References: | 23 |
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