Some results of transitivity for QTAG-modules

Abstract

For γ an ordinal number, we investigate the conditions on a QTAG-module M which will insure that M is transitive (fully transitive) whenever H_γ(M) is transitive (fully transitive). Specifically, we show that if M/H_γ(M) is a direct sum of countably generated modules and H_γ(M) is fully transitive, then M is fully transitive. The same result is established for transitivity except that  is restricted to be a countable ordinal. We also show that M is transitive if H_γ(M) is transitive, whenever M/H_γ(M) is totally projective and γ is an ordinal number. It is found that there exist QTAG-modules that are not potentially transitive.