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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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2016 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/155747 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862729080231690240 |
|---|---|
| author | Mutlu, F.T. |
| author_facet | Mutlu, F.T. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-12-07T19:12:21Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-155747 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T19:12:21Z |
| publishDate | 2016 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Amply (weakly) Goldie-Rad-supplemented modules Mutlu, F.T. |
| title | 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_short | Amply (weakly) Goldie-Rad-supplemented modules |
| title_sort | amply (weakly) goldie-rad-supplemented modules |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155747 |
| work_keys_str_mv | AT mutluft amplyweaklygoldieradsupplementedmodules |