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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...
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Інститут прикладної математики і механіки НАН України
2020
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/188555 |
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irk-123456789-1885552023-03-06T01:27:01Z F-supplemented modules Özdemir, S. 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. 2020 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/188555 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
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English |
| 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. |
| format |
Article |
| author |
Özdemir, S. |
| spellingShingle |
Özdemir, S. F-supplemented modules Algebra and Discrete Mathematics |
| author_facet |
Özdemir, S. |
| author_sort |
Özdemir, S. |
| title |
F-supplemented modules |
| title_short |
F-supplemented modules |
| title_full |
F-supplemented modules |
| title_fullStr |
F-supplemented modules |
| title_full_unstemmed |
F-supplemented modules |
| title_sort |
f-supplemented modules |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2020 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/188555 |
| citation_txt |
F-supplemented modules / S. Özdemir // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 83–96. — Бібліогр.: 6 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT ozdemirs fsupplementedmodules |
| first_indexed |
2023-10-18T23:08:38Z |
| last_indexed |
2023-10-18T23:08:38Z |
| _version_ |
1796157360526327808 |