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 Loc⊕ M (w 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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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 2, pp. 183–189, February, 2010.
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Nisanci, B., Pancar, A. On generalization of ⊕-cofinitely supplemented modules. Ukr Math J 62, 203–209 (2010). https://doi.org/10.1007/s11253-010-0344-4
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DOI: https://doi.org/10.1007/s11253-010-0344-4