QTAG torsionfree modules
The structure theory of abelian -groups does not depend on the properties of the ring of integers, in general. The substantial portion of this theory is based on the fact that a finitely generated -group is a direct sum of cyclics. Given a hereditary torsion theory on the category -Mod of unitary left -modules we can investigate torsionfree modules having the corresponding property for all torsionfree factor-modules (and a natural requirement concerning extensions of some homomorphisms). This...