Some Variations of δ-Supplemented Modules with Regard to a Hereditary Torsion Theory

Abstract

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