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 δ τ -small submodules. On this basis, the concepts of δ τ -lifting modules, δ τ -supplemented modules, and amply δ τ -supplemented modules and their fundamental properties are given, respectively. Furthermore, we present δ τ -semiperfect modules and give a characterization for them via (amply) δ τ -supplemented modules. Even we supply binary relations between these new module classes.