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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Lugansk National Taras Shevchenko University
2020
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admjournalluguniveduua-article-5852020-07-08T07:13:20Z Generalized 2-absorbing and strongly generalized 2-absorbing second submodules Ansari-Toroghy, H. Farshadifar, F. Maleki-Roudposhti, S. second, generalized 2-absorbing second 13C13, 13C99 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. Lugansk National Taras Shevchenko University 2020-07-08 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/585 10.12958/adm585 Algebra and Discrete Mathematics; Vol 29, No 2 (2020) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/585/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/585/270 Copyright (c) 2020 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2020-07-08T07:13:20Z |
| collection |
OJS |
| language |
English |
| topic |
second generalized 2-absorbing second 13C13 13C99 |
| spellingShingle |
second generalized 2-absorbing second 13C13 13C99 Ansari-Toroghy, H. Farshadifar, F. Maleki-Roudposhti, S. Generalized 2-absorbing and strongly generalized 2-absorbing second submodules |
| topic_facet |
second generalized 2-absorbing second 13C13 13C99 |
| format |
Article |
| author |
Ansari-Toroghy, H. Farshadifar, F. Maleki-Roudposhti, S. |
| author_facet |
Ansari-Toroghy, H. Farshadifar, F. Maleki-Roudposhti, S. |
| author_sort |
Ansari-Toroghy, H. |
| title |
Generalized 2-absorbing and strongly generalized 2-absorbing second submodules |
| title_short |
Generalized 2-absorbing and strongly generalized 2-absorbing second submodules |
| title_full |
Generalized 2-absorbing and strongly generalized 2-absorbing second submodules |
| title_fullStr |
Generalized 2-absorbing and strongly generalized 2-absorbing second submodules |
| title_full_unstemmed |
Generalized 2-absorbing and strongly generalized 2-absorbing second submodules |
| title_sort |
generalized 2-absorbing and strongly generalized 2-absorbing second submodules |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2020 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/585 |
| work_keys_str_mv |
AT ansaritoroghyh generalized2absorbingandstronglygeneralized2absorbingsecondsubmodules AT farshadifarf generalized2absorbingandstronglygeneralized2absorbingsecondsubmodules AT malekiroudposhtis generalized2absorbingandstronglygeneralized2absorbingsecondsubmodules |
| first_indexed |
2025-12-02T15:26:58Z |
| last_indexed |
2025-12-02T15:26:58Z |
| _version_ |
1850411875064348672 |