2017
Том 69
№ 9

# On generalization of $⊕$-cofinitely supplemented modules

Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 2, pp 183–189.

Citation Example: Nisanci B., Pancar A. On generalization of $⊕$-cofinitely supplemented modules // Ukr. Mat. Zh. - 2010. - 62, № 2. - pp. 183–189.

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