Generalized 2-absorbing and strongly generalized 2-absorbing second submodules
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 \(abm \in N\) for some \(a, b \in R\) and \(m \in M\), then \(am \in N\) or \(bm \in N\) or \(ab \in (N :_R M)\). In [3], the authors introduce...
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| Дата: | 2020 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2020
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/585 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | 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 \(abm \in N\) for some \(a, b \in R\) and \(m \in M\), then \(am \in N\) or \(bm \in N\) or \(ab \in (N :_R M)\). 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. |
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