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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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2016
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| Zitieren: | Amply (weakly) Goldie-Rad-supplemented modules / F.T. Mutlu // Algebra and Discrete Mathematics. — 2016. — Vol. 22, № 1. — С. 94-101. — Бібліогр.: 6 назв. — англ. |
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Mutlu, F.T. 2019-06-17T11:40:13Z 2019-06-17T11:40:13Z 2016 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. https://nasplib.isofts.kiev.ua/handle/123456789/155747 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. This study was supported by Anadolu University Scientific Research Projects Commission under the grant no:1505F225. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Amply (weakly) Goldie-Rad-supplemented modules Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Amply (weakly) Goldie-Rad-supplemented modules |
| spellingShingle |
Amply (weakly) Goldie-Rad-supplemented modules Mutlu, F.T. |
| 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 |
| author |
Mutlu, F.T. |
| author_facet |
Mutlu, F.T. |
| publishDate |
2016 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.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. |
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2025-12-07T19:12:21Z |
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2025-12-07T19:12:21Z |
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1850877926338199552 |