On preradicals associated to principal functors of module categories. III

The classes of modules and preradicals associated to the functor $Hom_R(-,U)$ are studied, continuing the investigations of parts I and II. The properties of classes of modules and of associated preradicals are shown, as well as the relations between preradicals. A similarity with the case of functor $T=U\otimes_{S^-}$ is explained.