A Note on ⊕-Cofinitely Supplemented Modules
Let R be a ring and M a right R-module. In this note, we show that a quotient of an ⊕-cofinitely supplemented module is not in general ⊕-cofinitely supplemented and prove that if a module M is an ⊕-cofinitely supplemented multiplication module with Rad(M)≪M, then M can be written as an irredundant s...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/10836 |
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| _version_ | 1832567380240236544 |
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| author | Yongduo Wang Qing Sun |
| author_facet | Yongduo Wang Qing Sun |
| author_sort | Yongduo Wang |
| collection | DOAJ |
| description | Let R be a ring and M a right R-module. In this note, we show that a quotient of an ⊕-cofinitely supplemented module is not in general ⊕-cofinitely supplemented and prove that if a module M is an ⊕-cofinitely supplemented multiplication module with Rad(M)≪M, then M can be written as an irredundant sum of local direct summand of M. An extension of the result of Calisici and Pancar [1], here it is shown that an arbitrary module is cofinitely semiperfect if and only if it is an (amply) cofinitely supplemented by supplements which have projective covers. |
| format | Article |
| id | doaj-art-84f251444f214a6f9680c0dccb94a738 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-84f251444f214a6f9680c0dccb94a7382025-02-03T01:01:37ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/1083610836A Note on ⊕-Cofinitely Supplemented ModulesYongduo Wang0Qing Sun1Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, ChinaDepartment of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, ChinaLet R be a ring and M a right R-module. In this note, we show that a quotient of an ⊕-cofinitely supplemented module is not in general ⊕-cofinitely supplemented and prove that if a module M is an ⊕-cofinitely supplemented multiplication module with Rad(M)≪M, then M can be written as an irredundant sum of local direct summand of M. An extension of the result of Calisici and Pancar [1], here it is shown that an arbitrary module is cofinitely semiperfect if and only if it is an (amply) cofinitely supplemented by supplements which have projective covers.http://dx.doi.org/10.1155/2007/10836 |
| spellingShingle | Yongduo Wang Qing Sun A Note on ⊕-Cofinitely Supplemented Modules International Journal of Mathematics and Mathematical Sciences |
| title | A Note on ⊕-Cofinitely Supplemented Modules |
| title_full | A Note on ⊕-Cofinitely Supplemented Modules |
| title_fullStr | A Note on ⊕-Cofinitely Supplemented Modules |
| title_full_unstemmed | A Note on ⊕-Cofinitely Supplemented Modules |
| title_short | A Note on ⊕-Cofinitely Supplemented Modules |
| title_sort | note on ⊕ cofinitely supplemented modules |
| url | http://dx.doi.org/10.1155/2007/10836 |
| work_keys_str_mv | AT yongduowang anoteoncofinitelysupplementedmodules AT qingsun anoteoncofinitelysupplementedmodules AT yongduowang noteoncofinitelysupplementedmodules AT qingsun noteoncofinitelysupplementedmodules |