Abstract
An h-reduced QT AG-module M is called totally projective if it has a nice system. Suppose M is a QT AG-module and K subset of M such that M/K is countably generated. If K belongs to any fixed sort of QT AG-modules, then does this imply that M belongs to the same module sort? The aim of the present article is to settle the question for certain kinds of modules, when a fixed sort of QT AG-modules coincides with the class of all totally projective QT AG-modules.