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 $\delta$ -supplemented modules via a hereditary torsion theory $\tau$ . With this aim, first, we define ${\delta }_{\tau }$ -small submodules. On this basis, the concepts of ${\delta }_{\tau }$ -lifting modules, ${\delta }_{\tau }$ -supplemented modules, and amply ${\delta }_{\tau }$ -supplemented modules and their fundamental properties are given, respectively. Furthermore, we present ${\delta }_{\tau }$ -semiperfect modules and give a characterization for them via (amply) ${\delta }_{\tau }$ -supplemented modules. Even we supply binary relations between these new module classes.