Modules which have a rad-supplement that is a direct summand in every extension
In this paper, we introduce the concept of modules with the properties (RE) and (SRE), and we provide various properties of these modules. In particular,we prove that a semisimple module M is Rad-supplementing if and only if M has the property (SRE). Moreover, we show that a ring R is a left V-ring...
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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/123456789/188355 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Modules which have a rad-supplement that is a direct summand in every extension / B.N. Türkmen, E. Türkmen // Algebra and Discrete Mathematics. — 2018. — Vol. 25, № 1. — С. 157-164. — Бібліогр.: 12 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862669136189980672 |
|---|---|
| author | Türkmen, B.N. Türkmen, E. |
| author_facet | Türkmen, B.N. Türkmen, E. |
| citation_txt | Modules which have a rad-supplement that is a direct summand in every extension / B.N. Türkmen, E. Türkmen // Algebra and Discrete Mathematics. — 2018. — Vol. 25, № 1. — С. 157-164. — Бібліогр.: 12 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | In this paper, we introduce the concept of modules with the properties (RE) and (SRE), and we provide various properties of these modules. In particular,we prove that a semisimple module M is Rad-supplementing if and only if M has the property (SRE). Moreover, we show that a ring R is a left V-ring if and only if every left R-module with the property (RE) is injective. Finally, we characterize the rings whose modules have the properties (RE) and (SRE).
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| first_indexed | 2025-12-07T15:26:45Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188355 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T15:26:45Z |
| publishDate | 2018 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Türkmen, B.N. Türkmen, E. 2023-02-23T19:42:28Z 2023-02-23T19:42:28Z 2018 Modules which have a rad-supplement that is a direct summand in every extension / B.N. Türkmen, E. Türkmen // Algebra and Discrete Mathematics. — 2018. — Vol. 25, № 1. — С. 157-164. — Бібліогр.: 12 назв. — англ. 1726-3255 2010 MSC: 16D10, 16D50, 16N80. https://nasplib.isofts.kiev.ua/handle/123456789/188355 In this paper, we introduce the concept of modules with the properties (RE) and (SRE), and we provide various properties of these modules. In particular,we prove that a semisimple module M is Rad-supplementing if and only if M has the property (SRE). Moreover, we show that a ring R is a left V-ring if and only if every left R-module with the property (RE) is injective. Finally, we characterize the rings whose modules have the properties (RE) and (SRE). The authors sincerely thank the referee for many valuable suggestions and comments in the revision of this paper. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Modules which have a rad-supplement that is a direct summand in every extension Article published earlier |
| spellingShingle | Modules which have a rad-supplement that is a direct summand in every extension Türkmen, B.N. Türkmen, E. |
| title | Modules which have a rad-supplement that is a direct summand in every extension |
| title_full | Modules which have a rad-supplement that is a direct summand in every extension |
| title_fullStr | Modules which have a rad-supplement that is a direct summand in every extension |
| title_full_unstemmed | Modules which have a rad-supplement that is a direct summand in every extension |
| title_short | Modules which have a rad-supplement that is a direct summand in every extension |
| title_sort | modules which have a rad-supplement that is a direct summand in every extension |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188355 |
| work_keys_str_mv | AT turkmenbn moduleswhichhavearadsupplementthatisadirectsummandineveryextension AT turkmene moduleswhichhavearadsupplementthatisadirectsummandineveryextension |