Generalized ⊕-Radical Supplemented Modules

Calisici and Turkmen called a module generalized -supplemented if every submodule has a generalized supplement that is a direct summand of . 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 is generalized -radical supplemented if and only if is generalized -radical supplemented. We completely determine the structure of these modules over left -rings. Moreover, we characterize semiperfect rings via generalized -radical supplemented modules.