F-supplemented modules
Let R be a ring, let M be a left R-module, and let U, V, F be submodules of M with F proper. We call V an F-supplement of U in M if V is minimal in the set F ⊆ X ⊆ M such that U+X = M, or equivalently, F ⊆ V , U+V = M and U∩V is F-small in V . If every submodule of M has an F-supplement, then we ca...
Збережено в:
| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2020 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2020
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/188555 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | F-supplemented modules / S. Özdemir // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 83–96. — Бібліогр.: 6 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862706989332692992 |
|---|---|
| author | Özdemir, S. |
| author_facet | Özdemir, S. |
| citation_txt | F-supplemented modules / S. Özdemir // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 83–96. — Бібліогр.: 6 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | Let R be a ring, let M be a left R-module, and let U, V, F be submodules of M with F proper. We call V an F-supplement of U in M if V is minimal in the set F ⊆ X ⊆ M such that U+X = M, or equivalently, F ⊆ V , U+V = M and U∩V is F-small in V . If every submodule of M has an F-supplement, then we call M an F-supplemented module. In this paper, we introduce and investigate F-supplement submodules and (amply) F-supplemented modules. We give some properties of these modules, and characterize finitely generated (amply) F-supplemented modules in terms of their certain submodules.
|
| first_indexed | 2025-12-07T17:02:58Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188555 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T17:02:58Z |
| publishDate | 2020 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Özdemir, S. 2023-03-05T17:32:23Z 2023-03-05T17:32:23Z 2020 F-supplemented modules / S. Özdemir // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 83–96. — Бібліогр.: 6 назв. — англ. 1726-3255 DOI:10.12958/adm1185 2010 MSC: 16D10, 16D80. https://nasplib.isofts.kiev.ua/handle/123456789/188555 Let R be a ring, let M be a left R-module, and let U, V, F be submodules of M with F proper. We call V an F-supplement of U in M if V is minimal in the set F ⊆ X ⊆ M such that U+X = M, or equivalently, F ⊆ V , U+V = M and U∩V is F-small in V . If every submodule of M has an F-supplement, then we call M an F-supplemented module. In this paper, we introduce and investigate F-supplement submodules and (amply) F-supplemented modules. We give some properties of these modules, and characterize finitely generated (amply) F-supplemented modules in terms of their certain submodules. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics F-supplemented modules Article published earlier |
| spellingShingle | F-supplemented modules Özdemir, S. |
| title | F-supplemented modules |
| title_full | F-supplemented modules |
| title_fullStr | F-supplemented modules |
| title_full_unstemmed | F-supplemented modules |
| title_short | F-supplemented modules |
| title_sort | f-supplemented modules |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188555 |
| work_keys_str_mv | AT ozdemirs fsupplementedmodules |