On Some \(QTAG\)-Modules

Abstract

In this paper we study totally projective \(QTAG\)-modules and the extensions of bounded  \(QTAG\)-modules. In the first section we study totally projective modules \(M/N\) and \(M'/N'\) where \(N, N'\) are isomorphic nice submodules of \(M\) and \(M'\) respectively. In fact the height preserving isomorphism between nice submodules is extented to the isomorphism from \(M\) onto \(M'\) with the help of Ulm -Kaplansky invariants. In the second section extensions of the bounded  \(QTAG\)-modules are studied. Here the invariants are automorphisms of bounded submodules of the extending module together with the cardinality of the minimal generating set of maximal summand of the extension module. The equivalence of epimorphisms is the main tool in this study.