Summability and direct sum of uniserial modules

Given the significance of abelian $p$-groups in module theory and their connection to algebraic structures, this paper focuses on constructing the $QTAG$-modules using the notion of torsion abelian groups and investigating their algebraic counterparts. These include examining specific types of submodules, such as isotype submodules, high submodules, and $h$-pure submodules, as well as exploring the concept of subsocles. In addition, we analyze the relationship between the concept of summability and the direct sum of uniserial modules within the context of these $QTAG$-modules.