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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| Date: | 2020 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2020
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/585 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543311190294528 |
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| author | Ansari-Toroghy, H. Farshadifar, F. Maleki-Roudposhti, S. |
| author_facet | Ansari-Toroghy, H. Farshadifar, F. Maleki-Roudposhti, S. |
| author_sort | Ansari-Toroghy, H. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2020-07-08T07:13:20Z |
| 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. |
| first_indexed | 2025-12-02T15:26:58Z |
| format | Article |
| id | admjournalluguniveduua-article-585 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:26:58Z |
| publishDate | 2020 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | 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 |
| 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 |
| title | 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_short | Generalized 2-absorbing and strongly generalized 2-absorbing second submodules |
| title_sort | generalized 2-absorbing and strongly generalized 2-absorbing second submodules |
| topic | second generalized 2-absorbing second 13C13 13C99 |
| topic_facet | second generalized 2-absorbing second 13C13 13C99 |
| 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 |