Modules in which every surjective endomorphism has a δ-small kernel
In this paper,we introduce the notion of δ-Hopfian modules. We give some properties of these modules and provide a characterization of semisimple rings in terms of δ-Hopfian modules by proving that a ring R is semisimple if and only if every R-module is δ-Hopfian. Also, we show that for a ring R, δ(...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2018 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2018
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/188409 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Modules in which every surjective endomorphism has a δ-small kernel / S. Ebrahimi Atani, M. Khoramdel, S. Dolati Pishhesari // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 2. — С. 170–189. — Бібліогр.: 18 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862661321421488128 |
|---|---|
| author | Ebrahimi Atani, S. Khoramdel, M. Dolati Pishhesari, S. |
| author_facet | Ebrahimi Atani, S. Khoramdel, M. Dolati Pishhesari, S. |
| citation_txt | Modules in which every surjective endomorphism has a δ-small kernel / S. Ebrahimi Atani, M. Khoramdel, S. Dolati Pishhesari // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 2. — С. 170–189. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | In this paper,we introduce the notion of δ-Hopfian modules. We give some properties of these modules and provide a characterization of semisimple rings in terms of δ-Hopfian modules by proving that a ring R is semisimple if and only if every R-module is δ-Hopfian. Also, we show that for a ring R, δ(R) = J(R) if and only if for all R-modules, the conditions δ-Hopfian and generalized Hopfian are equivalent. Moreover, we prove that δ-Hopfian property is a Morita invariant. Further, the δ-Hopficity of modules over truncated polynomial and triangular matrix rings are considered.
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| first_indexed | 2025-12-02T12:05:36Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188409 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-02T12:05:36Z |
| publishDate | 2018 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Ebrahimi Atani, S. Khoramdel, M. Dolati Pishhesari, S. 2023-02-27T15:51:56Z 2023-02-27T15:51:56Z 2018 Modules in which every surjective endomorphism has a δ-small kernel / S. Ebrahimi Atani, M. Khoramdel, S. Dolati Pishhesari // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 2. — С. 170–189. — Бібліогр.: 18 назв. — англ. 1726-3255 2010 MSC: 16D10, 16D40, 16D90. https://nasplib.isofts.kiev.ua/handle/123456789/188409 In this paper,we introduce the notion of δ-Hopfian modules. We give some properties of these modules and provide a characterization of semisimple rings in terms of δ-Hopfian modules by proving that a ring R is semisimple if and only if every R-module is δ-Hopfian. Also, we show that for a ring R, δ(R) = J(R) if and only if for all R-modules, the conditions δ-Hopfian and generalized Hopfian are equivalent. Moreover, we prove that δ-Hopfian property is a Morita invariant. Further, the δ-Hopficity of modules over truncated polynomial and triangular matrix rings are considered. The authors express their deep gratitude to the referee for her/his helpful suggestions for the improvement of this work. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Modules in which every surjective endomorphism has a δ-small kernel Article published earlier |
| spellingShingle | Modules in which every surjective endomorphism has a δ-small kernel Ebrahimi Atani, S. Khoramdel, M. Dolati Pishhesari, S. |
| title | Modules in which every surjective endomorphism has a δ-small kernel |
| title_full | Modules in which every surjective endomorphism has a δ-small kernel |
| title_fullStr | Modules in which every surjective endomorphism has a δ-small kernel |
| title_full_unstemmed | Modules in which every surjective endomorphism has a δ-small kernel |
| title_short | Modules in which every surjective endomorphism has a δ-small kernel |
| title_sort | modules in which every surjective endomorphism has a δ-small kernel |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188409 |
| work_keys_str_mv | AT ebrahimiatanis modulesinwhicheverysurjectiveendomorphismhasaδsmallkernel AT khoramdelm modulesinwhicheverysurjectiveendomorphismhasaδsmallkernel AT dolatipishhesaris modulesinwhicheverysurjectiveendomorphismhasaδsmallkernel |