Abstract
In this work we will attempt to define and investigate new classes of modules named -g-supplemented and -g-radical supplemented as a proper generalization of class of g-lifting modules and identify several distinct characterizations of these modules. Additionally, we'll attempt to explain the concepts of projective g-covers and g-semiperfect modules. It is shown that the two buildings of g-semiperfect and -g-supplemented modules are the same for the class of projective modules.
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