ON ∗-BASES FOR QT AG-MODULES

Abstract

An h-reduced QTAG-module M is called totally projective if it has a nice system. In this paper, we find a new characterization for totally projective QTAG-modules of cardinality not exceeding ℵ1. This is in terms of the existence of a certain kind of basis which is called a ∗-basis. The question about the structure of larger modules having a ∗-basis is left open, but we establish some closure properties of such modules. We also study secure submodules with the help of these ∗-bases and prove
that every secure submodule is nice