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...
Gespeichert in:
| Veröffentlicht in: | Algebra and Discrete Mathematics |
|---|---|
| Datum: | 2020 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2020
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/188555 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | F-supplemented modules / S. Özdemir // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 83–96. — Бібліогр.: 6 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-188555 |
|---|---|
| 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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
F-supplemented modules |
| spellingShingle |
F-supplemented modules Özdemir, S. |
| 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 |
| author |
Özdemir, S. |
| author_facet |
Özdemir, S. |
| publishDate |
2020 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.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. |
| work_keys_str_mv |
AT ozdemirs fsupplementedmodules |
| first_indexed |
2025-12-07T17:02:58Z |
| last_indexed |
2025-12-07T17:02:58Z |
| _version_ |
1850869786618101760 |