On generalization of $⊕$-cofinitely supplemented modules
We study the properties of ⊕-cofinitely radical supplemented modules, or, briefly, $cgs^{⊕}$-modules. It is shown that a module with summand sum property (SSP) is $cgs^{⊕}$ if and only if $M/w \text{Loc}^{⊕} M$ ($w \text{Loc}^{⊕} M$ is the sum of all $w$-local direct summands of a module $M$) does n...
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| Date: | 2010 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2010
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2854 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We study the properties of ⊕-cofinitely radical supplemented modules, or, briefly, $cgs^{⊕}$-modules. It is shown that a module with summand sum property (SSP) is $cgs^{⊕}$ if and only if $M/w \text{Loc}^{⊕} M$ ($w \text{Loc}^{⊕} M$ is the sum of all $w$-local direct summands of a module $M$) does not contain any maximal submodule, that every cofinite direct summand of a UC-extending $cgs^{⊕}$-module is $cgs^{⊕}$, and that, for any ring $R$, every free $R$-module is $cgs^{⊕}$ if and only if $R$ is semiperfect. |
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