On QTAG-modules containing proper h-purity

Abstract

There are numerous problems of determining the QTAG-modules in which every h-pure submodule is isotype or the QTAG-modules in which every submodule is isotype. Our global aim here is to find in this direction a new problem by generalizing the h-purity in QTAG-modules, and thereby to establish some characterizations of the QTAG-modules in which every σ-pure submodule is λ-pure submodule for arbitrary ordinals σ and λ.