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: | English |
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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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oai:ojs.admjournal.luguniv.edu.ua: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 |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
Dedekind finite modules Hopfian modules generalized Hopfian modules \(\delta\)-Hopfian modules 16D10 16D40 16D90 |
| 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 |
| topic_facet |
Dedekind finite modules Hopfian modules generalized Hopfian modules \(\delta\)-Hopfian modules 16D10 16D40 16D90 |
| format |
Article |
| author |
Ebrahimi Atani, Shahabaddin Khoramdel, Mehdi Dolati Pishhesari, Saboura |
| author_facet |
Ebrahimi Atani, Shahabaddin Khoramdel, Mehdi Dolati Pishhesari, Saboura |
| author_sort |
Ebrahimi Atani, Shahabaddin |
| title |
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_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_sort |
modules in which every surjective endomorphism has a \(\delta\)-small kernel |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2019 |
| 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 |
| first_indexed |
2024-04-12T06:25:17Z |
| last_indexed |
2024-04-12T06:25:17Z |
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