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Amply (weakly) Goldie-Rad-supplemented modules
Let R be a ring and M be a right R-module. We say a submodule S of M is a \textit{(weak) Goldie-Rad-supplement} of a submodule N in M, if M=N+S, (N∩S≤Rad(M)) N∩S≤Rad(S) and Nβ∗∗S, and M is called amply (weakly) Goldie-Rad-supplemented if every submodule of M has ample (weak) Goldie-Rad-supplements...
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Інститут прикладної математики і механіки НАН України
2016
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/155747 |
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irk-123456789-1557472019-06-18T01:25:36Z Amply (weakly) Goldie-Rad-supplemented modules Mutlu, F.T. Let R be a ring and M be a right R-module. We say a submodule S of M is a \textit{(weak) Goldie-Rad-supplement} of a submodule N in M, if M=N+S, (N∩S≤Rad(M)) N∩S≤Rad(S) and Nβ∗∗S, and M is called amply (weakly) Goldie-Rad-supplemented if every submodule of M has ample (weak) Goldie-Rad-supplements in M. In this paper we study various properties of such modules. We show that every distributive projective weakly Goldie-Rad-Supplemented module is amply weakly Goldie-Rad-Supplemented. We also show that if M is amply (weakly) Goldie-Rad-supplemented and satisfies DCC on (weak) Goldie-Rad-supplement submodules and on small submodules, then M is Artinian. 2016 Article Amply (weakly) Goldie-Rad-supplemented modules / F.T. Mutlu // Algebra and Discrete Mathematics. — 2016. — Vol. 22, № 1. — С. 94-101. — Бібліогр.: 6 назв. — англ. 1726-3255 2010 MSC:16D10, 16D40, 16D70. http://dspace.nbuv.gov.ua/handle/123456789/155747 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
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English |
| description |
Let R be a ring and M be a right R-module. We say a submodule S of M is a \textit{(weak) Goldie-Rad-supplement} of a submodule N in M, if M=N+S, (N∩S≤Rad(M)) N∩S≤Rad(S) and Nβ∗∗S, and M is called amply (weakly) Goldie-Rad-supplemented if every submodule of M has ample (weak) Goldie-Rad-supplements in M. In this paper we study various properties of such modules. We show that every distributive projective weakly Goldie-Rad-Supplemented module is amply weakly Goldie-Rad-Supplemented. We also show that if M is amply (weakly) Goldie-Rad-supplemented and satisfies DCC on (weak) Goldie-Rad-supplement submodules and on small submodules, then M is Artinian. |
| format |
Article |
| author |
Mutlu, F.T. |
| spellingShingle |
Mutlu, F.T. Amply (weakly) Goldie-Rad-supplemented modules Algebra and Discrete Mathematics |
| author_facet |
Mutlu, F.T. |
| author_sort |
Mutlu, F.T. |
| title |
Amply (weakly) Goldie-Rad-supplemented modules |
| title_short |
Amply (weakly) Goldie-Rad-supplemented modules |
| title_full |
Amply (weakly) Goldie-Rad-supplemented modules |
| title_fullStr |
Amply (weakly) Goldie-Rad-supplemented modules |
| title_full_unstemmed |
Amply (weakly) Goldie-Rad-supplemented modules |
| title_sort |
amply (weakly) goldie-rad-supplemented modules |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/155747 |
| citation_txt |
Amply (weakly) Goldie-Rad-supplemented modules / F.T. Mutlu // Algebra and Discrete Mathematics. — 2016. — Vol. 22, № 1. — С. 94-101. — Бібліогр.: 6 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT mutluft amplyweaklygoldieradsupplementedmodules |
| first_indexed |
2023-05-20T17:47:39Z |
| last_indexed |
2023-05-20T17:47:39Z |
| _version_ |
1796154099461259264 |