Some Generalizations of g-lifting Modules

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.

${\rm ({P_g}^*)}$-modules

“…If each submodule of ∈ Mod-ℜ has a g-radical supplement, then is called g-radical supplemented see [6]. If each submodule of has a g-radical supplement which is a direct summand of , Ghawi [2] calls it ⨁-g-radical supplemented. He also introduced the definition of (P * )-modules in the same article, but this was not the author's main concern in the paper.…”