On totally projective QTAG-modules characterized by its submodules

Abstract

A $QTAG$-module $M$ is called almost totally projective if it has a weak nice system. Here we show that the isotype submodules of a totally projective module which are almost totally projective are precisely those that are separable. From this characterization it follows that every balanced submodule of a totally projective module is almost totally projective. Finally, in some special cases we settle the question of whether a direct summand of an almost totally projective module is again almost totally projective.