Jacobson Hopfian modules
The study of modules by properties of their endomorphisms has long been of interest. In this paper we introduce a proper generalization of that of Hopfian modules, called Jacobson Hopfian modules. A right \(R\)-module \(M\) is said to be Jacobson Hopfian, if any surjective endomorphism of \(M\) has...
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| Дата: | 2022 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2022
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1842 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543055119646720 |
|---|---|
| author | El Moussaouy, A. Moniri Hamzekolaee, A. Ziane, M. |
| author_facet | El Moussaouy, A. Moniri Hamzekolaee, A. Ziane, M. |
| author_sort | El Moussaouy, A. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2022-06-15T04:49:44Z |
| description | The study of modules by properties of their endomorphisms has long been of interest. In this paper we introduce a proper generalization of that of Hopfian modules, called Jacobson Hopfian modules. A right \(R\)-module \(M\) is said to be Jacobson Hopfian, if any surjective endomorphism of \(M\) has a Jacobson-small kernel. We characterize the rings \(R\) for which every finitely generated free \(R\)-module is Jacobson Hopfian. We prove that a ring \(R\) is semisimple if and only if every \(R\)-module is Jacobson Hopfian. Some other properties and characterizations of Jacobson Hopfian modules are also obtained with examples. Further, we prove that the Jacobson Hopfian property is preserved under Morita equivalences. |
| first_indexed | 2025-12-02T15:50:06Z |
| format | Article |
| id | admjournalluguniveduua-article-1842 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:50:06Z |
| publishDate | 2022 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-18422022-06-15T04:49:44Z Jacobson Hopfian modules El Moussaouy, A. Moniri Hamzekolaee, A. Ziane, M. Hopfian modules, generalized Hopfian modules, Jacobson Hopfian modules, Dedekind finite modules 16D10, 16D40, 16D90 The study of modules by properties of their endomorphisms has long been of interest. In this paper we introduce a proper generalization of that of Hopfian modules, called Jacobson Hopfian modules. A right \(R\)-module \(M\) is said to be Jacobson Hopfian, if any surjective endomorphism of \(M\) has a Jacobson-small kernel. We characterize the rings \(R\) for which every finitely generated free \(R\)-module is Jacobson Hopfian. We prove that a ring \(R\) is semisimple if and only if every \(R\)-module is Jacobson Hopfian. Some other properties and characterizations of Jacobson Hopfian modules are also obtained with examples. Further, we prove that the Jacobson Hopfian property is preserved under Morita equivalences. Lugansk National Taras Shevchenko University 2022-06-15 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1842 10.12958/adm1842 Algebra and Discrete Mathematics; Vol 33, No 1 (2022) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1842/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1842/891 Copyright (c) 2022 Algebra and Discrete Mathematics |
| spellingShingle | Hopfian modules generalized Hopfian modules, Jacobson Hopfian modules Dedekind finite modules 16D10 16D40 16D90 El Moussaouy, A. Moniri Hamzekolaee, A. Ziane, M. Jacobson Hopfian modules |
| title | Jacobson Hopfian modules |
| title_full | Jacobson Hopfian modules |
| title_fullStr | Jacobson Hopfian modules |
| title_full_unstemmed | Jacobson Hopfian modules |
| title_short | Jacobson Hopfian modules |
| title_sort | jacobson hopfian modules |
| topic | Hopfian modules generalized Hopfian modules, Jacobson Hopfian modules Dedekind finite modules 16D10 16D40 16D90 |
| topic_facet | Hopfian modules generalized Hopfian modules, Jacobson Hopfian modules Dedekind finite modules 16D10 16D40 16D90 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1842 |
| work_keys_str_mv | AT elmoussaouya jacobsonhopfianmodules AT monirihamzekolaeea jacobsonhopfianmodules AT zianem jacobsonhopfianmodules |