Abstract
Çalışıcı and Türkmen called a module M generalized ⊕-supplemented if every submodule has a generalized supplement that is a direct summand of M. Motivated by this, it is natural to introduce another notion that we called generalized ⊕-radical supplemented modules as a proper generalization of generalized ⊕-supplemented modules. In this paper, we obtain various properties of generalized ⊕-radical supplemented modules. We show that the class of generalized ⊕-radical supplemented modules is closed under finite direct sums. We attain that over a Dedekind domain a module M is generalized ⊕-radical supplemented if and only if M/P(M) is generalized ⊕-radical supplemented. We completely determine the structure of these modules over left V-rings. Moreover, we characterize semiperfect rings via generalized ⊕-radical supplemented modules.
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