A generalization of supplemented modules
Let R be an arbitrary ring with identity and M a right R-module. In this paper, we introduce a class of modules which is an analogous of δ-supplemented modules defined by Kosan. The module M is called principally δ-supplemented, for all m∈M there exists a submodule A of M with M=mR+A and (mR)∩A δ-...
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| Дата: | 2011 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2011
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/154837 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A generalization of supplemented modules / H. Inankil, S. Halıcıoglu, A. Harmanci // Algebra and Discrete Mathematics. — 2011. — Vol. 11, № 1. — С. 59–74 — Бібліогр.: 16 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1548372019-06-17T01:31:12Z A generalization of supplemented modules Inankil, H. Halıcıoglu, S. Harmanci, A. Let R be an arbitrary ring with identity and M a right R-module. In this paper, we introduce a class of modules which is an analogous of δ-supplemented modules defined by Kosan. The module M is called principally δ-supplemented, for all m∈M there exists a submodule A of M with M=mR+A and (mR)∩A δ-small in A. We prove that some results of δ-supplemented modules can be extended to principally δ-supplemented modules for this general settings. We supply some examples showing that there are principally δ-supplemented modules but not δ-supplemented. We also introduce principally δ-semiperfect modules as a generalization of δ-semiperfect modules and investigate their properties. 2011 Article A generalization of supplemented modules / H. Inankil, S. Halıcıoglu, A. Harmanci // Algebra and Discrete Mathematics. — 2011. — Vol. 11, № 1. — С. 59–74 — Бібліогр.: 16 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:16U80. http://dspace.nbuv.gov.ua/handle/123456789/154837 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Let R be an arbitrary ring with identity and M a right R-module. In this paper, we introduce a class of modules which is an analogous of δ-supplemented modules defined by Kosan. The module M is called principally δ-supplemented, for all m∈M there exists a submodule A of M with M=mR+A and (mR)∩A δ-small in A. We prove that some results of δ-supplemented modules can be extended to principally δ-supplemented modules for this general settings. We supply some examples showing that there are principally δ-supplemented modules but not δ-supplemented. We also introduce principally δ-semiperfect modules as a generalization of δ-semiperfect modules and investigate their properties. |
| format |
Article |
| author |
Inankil, H. Halıcıoglu, S. Harmanci, A. |
| spellingShingle |
Inankil, H. Halıcıoglu, S. Harmanci, A. A generalization of supplemented modules Algebra and Discrete Mathematics |
| author_facet |
Inankil, H. Halıcıoglu, S. Harmanci, A. |
| author_sort |
Inankil, H. |
| title |
A generalization of supplemented modules |
| title_short |
A generalization of supplemented modules |
| title_full |
A generalization of supplemented modules |
| title_fullStr |
A generalization of supplemented modules |
| title_full_unstemmed |
A generalization of supplemented modules |
| title_sort |
generalization of supplemented modules |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/154837 |
| citation_txt |
A generalization of supplemented modules / H. Inankil, S. Halıcıoglu, A. Harmanci // Algebra and Discrete Mathematics. — 2011. — Vol. 11, № 1. — С. 59–74 — Бібліогр.: 16 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
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2023-05-20T17:45:23Z |
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2023-05-20T17:45:23Z |
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