Modules in which every surjective endomorphism has a \(\delta\)-small kernel
In this paper, we introduce the notion of \(\delta\)-Hopfian modules. We give some properties of these modules and provide a~characterization of semisimple rings in terms of \(\delta\)-Hopfian modules by proving that a ring \(R\) is semisimple if and only if every \(R\)-module is \(\delta\)-Hopf...
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| Дата: | 2019 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2019
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/365 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543257931022336 |
|---|---|
| author | Ebrahimi Atani, Shahabaddin Khoramdel, Mehdi Dolati Pishhesari, Saboura |
| author_facet | Ebrahimi Atani, Shahabaddin Khoramdel, Mehdi Dolati Pishhesari, Saboura |
| author_sort | Ebrahimi Atani, Shahabaddin |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2019-01-24T08:21:31Z |
| description | In this paper, we introduce the notion of \(\delta\)-Hopfian modules. We give some properties of these modules and provide a~characterization of semisimple rings in terms of \(\delta\)-Hopfian modules by proving that a ring \(R\) is semisimple if and only if every \(R\)-module is \(\delta\)-Hopfian. Also, we show that for a ring \(R\), \(\delta(R)=J(R)\) if and only if for all \(R\)-modules, the conditions \(\delta\)-Hopfian and generalized Hopfian are equivalent. Moreover, we prove that \(\delta\)-Hopfian property is a Morita invariant. Further, the \(\delta\)-Hopficity of modules over truncated polynomial and triangular matrix rings are considered. |
| first_indexed | 2026-02-08T08:00:21Z |
| format | Article |
| id | admjournalluguniveduua-article-365 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T08:00:21Z |
| publishDate | 2019 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-3652019-01-24T08:21:31Z Modules in which every surjective endomorphism has a \(\delta\)-small kernel Ebrahimi Atani, Shahabaddin Khoramdel, Mehdi Dolati Pishhesari, Saboura Dedekind finite modules, Hopfian modules, generalized Hopfian modules, \(\delta\)-Hopfian modules 16D10, 16D40, 16D90 In this paper, we introduce the notion of \(\delta\)-Hopfian modules. We give some properties of these modules and provide a~characterization of semisimple rings in terms of \(\delta\)-Hopfian modules by proving that a ring \(R\) is semisimple if and only if every \(R\)-module is \(\delta\)-Hopfian. Also, we show that for a ring \(R\), \(\delta(R)=J(R)\) if and only if for all \(R\)-modules, the conditions \(\delta\)-Hopfian and generalized Hopfian are equivalent. Moreover, we prove that \(\delta\)-Hopfian property is a Morita invariant. Further, the \(\delta\)-Hopficity of modules over truncated polynomial and triangular matrix rings are considered. Lugansk National Taras Shevchenko University 2019-01-24 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/365 Algebra and Discrete Mathematics; Vol 26, No 2 (2018) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/365/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/365/150 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/365/444 Copyright (c) 2019 Algebra and Discrete Mathematics |
| spellingShingle | Dedekind finite modules Hopfian modules generalized Hopfian modules \(\delta\)-Hopfian modules 16D10 16D40 16D90 Ebrahimi Atani, Shahabaddin Khoramdel, Mehdi Dolati Pishhesari, Saboura Modules in which every surjective endomorphism has a \(\delta\)-small kernel |
| title | Modules in which every surjective endomorphism has a \(\delta\)-small kernel |
| title_full | Modules in which every surjective endomorphism has a \(\delta\)-small kernel |
| title_fullStr | Modules in which every surjective endomorphism has a \(\delta\)-small kernel |
| title_full_unstemmed | Modules in which every surjective endomorphism has a \(\delta\)-small kernel |
| title_short | Modules in which every surjective endomorphism has a \(\delta\)-small kernel |
| title_sort | modules in which every surjective endomorphism has a \(\delta\)-small kernel |
| topic | Dedekind finite modules Hopfian modules generalized Hopfian modules \(\delta\)-Hopfian modules 16D10 16D40 16D90 |
| topic_facet | Dedekind finite modules Hopfian modules generalized Hopfian modules \(\delta\)-Hopfian modules 16D10 16D40 16D90 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/365 |
| work_keys_str_mv | AT ebrahimiatanishahabaddin modulesinwhicheverysurjectiveendomorphismhasadeltasmallkernel AT khoramdelmehdi modulesinwhicheverysurjectiveendomorphismhasadeltasmallkernel AT dolatipishhesarisaboura modulesinwhicheverysurjectiveendomorphismhasadeltasmallkernel |