Countably Generated Extensions of QTAG-Modules

Abstract

Let the \(QTAG\)-module \(M\) be the set-theoretic union of a countable collection of isotype submodules \(S_k\) of countable length. For \(0 \leq k < \omega\) we prove that \(M\) is totally projective if \(S_k\) is totally projective. Certain related assertions in this direction are also presented.