In present work, we describe and investigate torsion theoretic versions of -supplemented modules via a hereditary torsion theory -. With this aim, 4rst, we de4ne --small submodules. On this basis, the concepts of --lifting modules, --supplemented modules, and amply --supplemented modules and their fundamental properties are given, respectively. Furthermore, we present --semiperfect modules and give a characterization for them via (amply) --supplemented modules. Even we supply binary relations between these new module classes.
