On totally projective QTAG-modules

A module M over an associative ring R with unity is a QTAG-module if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules. In this paper we investigate the class of QTAG-modules whose every separable module is a direct sum of uniserial modules; such modules are called ω-totally ω-projective. We discuss an interesting characterization of this class and we show that the class of $(\omega + n) $-totally $(\omega + n) $-projective modules contains the class of ω-totally ω-projective modules.