2019
Том 71
№ 11

All Issues

Nisanci B.

Articles: 1
Article (English)

On generalization of $⊕$-cofinitely supplemented modules

Nisanci B., Pancar A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 2. - pp. 183–189

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.