On Rad-D12 Modules
Let M be a right R-module. We call M Rad-D12, if for every sub- module N of M, there exist a direct summand K of M and an epimor- phism α : K → M/N such that Kererα ⊆ Rad(K). We show that a direct summand of a Rad-D12 module need not be a Rad-D12 module. We investigate completely Rad-D12 modules (mo...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2013-03-01
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| Series: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/auom-2013-0012 |
| _version_ | 1818308845627244544 |
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| author | Talebi Yahya Hamzekolaee Ali Reza Moniri Tütüncü Derya Keskin |
| author_facet | Talebi Yahya Hamzekolaee Ali Reza Moniri Tütüncü Derya Keskin |
| author_sort | Talebi Yahya |
| collection | DOAJ |
| description | Let M be a right R-module. We call M Rad-D12, if for every sub- module N of M, there exist a direct summand K of M and an epimor- phism α : K → M/N such that Kererα ⊆ Rad(K). We show that a direct summand of a Rad-D12 module need not be a Rad-D12 module. We investigate completely Rad-D12 modules (modules for which every direct summand is a Rad-D12 module). We also show that a direct sum of Rad-D12 modules need not be a Rad-D12 module. Then we deal with some cases of direct sums of Rad-D12 modules. |
| first_indexed | 2024-12-13T07:20:45Z |
| format | Article |
| id | doaj.art-036cd3a7f6314b118e87aeed0a2f320b |
| institution | Directory Open Access Journal |
| issn | 1844-0835 |
| language | English |
| last_indexed | 2024-12-13T07:20:45Z |
| publishDate | 2013-03-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| spelling | doaj.art-036cd3a7f6314b118e87aeed0a2f320b2022-12-21T23:55:26ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352013-03-0121120120810.2478/auom-2013-0012On Rad-D12 ModulesTalebi Yahya0Hamzekolaee Ali Reza Moniri1Tütüncü Derya Keskin2Department of Mathematics, University of Mazandaran, Babolsar, IranDepartment of Mathematics, University of Mazandaran, Babolsar, IranDepartment of Mathematics, University of Hacettepe, 06800 Beytepe, Ankara, TurkeyLet M be a right R-module. We call M Rad-D12, if for every sub- module N of M, there exist a direct summand K of M and an epimor- phism α : K → M/N such that Kererα ⊆ Rad(K). We show that a direct summand of a Rad-D12 module need not be a Rad-D12 module. We investigate completely Rad-D12 modules (modules for which every direct summand is a Rad-D12 module). We also show that a direct sum of Rad-D12 modules need not be a Rad-D12 module. Then we deal with some cases of direct sums of Rad-D12 modules.https://doi.org/10.2478/auom-2013-0012small submodulerad-⊕-supplemented modulerad-d12 modulesduo module |
| spellingShingle | Talebi Yahya Hamzekolaee Ali Reza Moniri Tütüncü Derya Keskin On Rad-D12 Modules Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica small submodule rad-⊕-supplemented module rad-d12 modules duo module |
| title | On Rad-D12 Modules |
| title_full | On Rad-D12 Modules |
| title_fullStr | On Rad-D12 Modules |
| title_full_unstemmed | On Rad-D12 Modules |
| title_short | On Rad-D12 Modules |
| title_sort | on rad d12 modules |
| topic | small submodule rad-⊕-supplemented module rad-d12 modules duo module |
| url | https://doi.org/10.2478/auom-2013-0012 |
| work_keys_str_mv | AT talebiyahya onradd12modules AT hamzekolaeealirezamoniri onradd12modules AT tutuncuderyakeskin onradd12modules |