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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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2011 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2011
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| Онлайн доступ: | https://nasplib.isofts.kiev.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| _version_ | 1862683662673248256 |
|---|---|
| author | Inankil, H. Halıcıoglu, S. Harmanci, A. |
| author_facet | Inankil, H. Halıcıoglu, S. Harmanci, A. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-12-07T15:57:00Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154837 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T15:57:00Z |
| publishDate | 2011 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Inankil, H. Halıcıoglu, S. Harmanci, A. 2019-06-16T05:39:07Z 2019-06-16T05:39:07Z 2011 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. https://nasplib.isofts.kiev.ua/handle/123456789/154837 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics A generalization of supplemented modules Article published earlier |
| spellingShingle | A generalization of supplemented modules Inankil, H. Halıcıoglu, S. Harmanci, A. |
| title | 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_short | A generalization of supplemented modules |
| title_sort | generalization of supplemented modules |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154837 |
| work_keys_str_mv | AT inankilh ageneralizationofsupplementedmodules AT halıcıoglus ageneralizationofsupplementedmodules AT harmancia ageneralizationofsupplementedmodules AT inankilh generalizationofsupplementedmodules AT halıcıoglus generalizationofsupplementedmodules AT harmancia generalizationofsupplementedmodules |