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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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2018
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| Schriftenreihe: | Algebra and Discrete Mathematics |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/188355 |
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| Zitieren: | 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. |
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irk-123456789-1883552023-02-24T01:27:32Z Modules which have a rad-supplement that is a direct summand in every extension Türkmen, B.N. Türkmen, E. 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). 2018 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/188355 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| 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). |
| format |
Article |
| author |
Türkmen, B.N. Türkmen, E. |
| spellingShingle |
Türkmen, B.N. Türkmen, E. Modules which have a rad-supplement that is a direct summand in every extension Algebra and Discrete Mathematics |
| author_facet |
Türkmen, B.N. Türkmen, E. |
| author_sort |
Türkmen, B.N. |
| title |
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_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_sort |
modules which have a rad-supplement that is a direct summand in every extension |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2018 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/188355 |
| 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. |
| series |
Algebra and Discrete Mathematics |
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2025-07-16T10:22:46Z |
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2025-07-16T10:22:46Z |
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