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 |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |