Abstract
The results for abelian groups can be generalized for modules after imposing some conditions on modules/rings. Here the rings are almost restriction free and the QTAG-modules satisfy a simple condition. In this paper essentially finitely indecomposable modules are studied with the help of h-pure and nice submodules and socles. HT-modules were defined by Mehdi et al. (On HT-modules, To appear in GAMS, 2015) and here we investigate the relation between HT-modules and essentially finitely indecomposable modules.