Abstract
Mehdi studied (w + k)-projective QTAG-modules with the help of their submodules contained in H-k(M) (the submodule generated by the elements of exponents at most k). These modules contain nice submodules N contained in H-k(M) such that M/ N is a direct sum of uniserial modules. Here, we investigate the class A of QTAG-modules, containing nice submodules N subset of H-k(M) such that M/N is totally projective. We also study strong. w-elongation of totally projective QTAG-modules by (w + k)-projective QTAG-modules.