Ukr. Mat. Zh. - 2015. - 67, № 6. - pp. 861–864
Following the concept of generalized small submodule, we define $g$ -supplemented modules and characterize some fundamental properties of these modules. Moreover, the generalized radical of a module is defined and the relationship between the generalized radical and the radical of a module is investigated. Finally, the definition of amply $g$ -supplemented modules is given with some basic properties of these modules.