\(F\)-supplemented modules
Let \(R\) be a ring, let \(M\) be a left \(R\)-module, and let \(U, V, F\) be submodules of \(M\) with \(F\) proper. We call \(V\) an \(F\)-supplement of \(U\) in \(M\) if \(V\) is minimal in the set \( F \subseteq X \subseteq M\) such that \( U + X = M\), or equivalently, \(F\subseteq V\), \(U + V...
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| Дата: | 2020 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2020
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1185 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543051458019328 |
|---|---|
| author | Özdemir, S. |
| author_facet | Özdemir, S. |
| author_sort | Özdemir, S. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2021-01-05T07:13:09Z |
| description | Let \(R\) be a ring, let \(M\) be a left \(R\)-module, and let \(U, V, F\) be submodules of \(M\) with \(F\) proper. We call \(V\) an \(F\)-supplement of \(U\) in \(M\) if \(V\) is minimal in the set \( F \subseteq X \subseteq M\) such that \( U + X = M\), or equivalently, \(F\subseteq V\), \(U + V = M\) and \(U \cap V \) is \(F\)-small in \( V\). If every submodule of \(M\) has an \(F\)-supplement, then we call \(M\) an \(F\)-supplemented module. In this paper, we introduce and investigate \(F\)-supplement submodules and (amply) \(F\)-supplemented modules. We give some properties of these modules, and characterize finitely generated (amply) \(F\)-supplemented modules in terms of their certain submodules. |
| first_indexed | 2025-12-02T15:29:53Z |
| format | Article |
| id | admjournalluguniveduua-article-1185 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:29:53Z |
| publishDate | 2020 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-11852021-01-05T07:13:09Z \(F\)-supplemented modules Özdemir, S. \(F\)-supplement and \(F\)-small submodules, \(F\)-supplemented, \(F\)-local and \(F\)-hollow modules 16D10, 16D80 Let \(R\) be a ring, let \(M\) be a left \(R\)-module, and let \(U, V, F\) be submodules of \(M\) with \(F\) proper. We call \(V\) an \(F\)-supplement of \(U\) in \(M\) if \(V\) is minimal in the set \( F \subseteq X \subseteq M\) such that \( U + X = M\), or equivalently, \(F\subseteq V\), \(U + V = M\) and \(U \cap V \) is \(F\)-small in \( V\). If every submodule of \(M\) has an \(F\)-supplement, then we call \(M\) an \(F\)-supplemented module. In this paper, we introduce and investigate \(F\)-supplement submodules and (amply) \(F\)-supplemented modules. We give some properties of these modules, and characterize finitely generated (amply) \(F\)-supplemented modules in terms of their certain submodules. Lugansk National Taras Shevchenko University 2020-12-30 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1185 10.12958/adm1185 Algebra and Discrete Mathematics; Vol 30, No 1 (2020) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1185/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1185/369 Copyright (c) 2020 Algebra and Discrete Mathematics |
| spellingShingle | \(F\)-supplement and \(F\)-small submodules \(F\)-supplemented \(F\)-local and \(F\)-hollow modules 16D10 16D80 Özdemir, S. \(F\)-supplemented modules |
| title | \(F\)-supplemented modules |
| title_full | \(F\)-supplemented modules |
| title_fullStr | \(F\)-supplemented modules |
| title_full_unstemmed | \(F\)-supplemented modules |
| title_short | \(F\)-supplemented modules |
| title_sort | \(f\)-supplemented modules |
| topic | \(F\)-supplement and \(F\)-small submodules \(F\)-supplemented \(F\)-local and \(F\)-hollow modules 16D10 16D80 |
| topic_facet | \(F\)-supplement and \(F\)-small submodules \(F\)-supplemented \(F\)-local and \(F\)-hollow modules 16D10 16D80 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1185 |
| work_keys_str_mv | AT ozdemirs fsupplementedmodules |