A projective characterization for SKT-modules

Abstract:

In this paper a class of abelian groups (SKT-modules), which includes the torsion totally projective groups, S-groups, and balanced projectives is shown to be a subclass of a projective class of groups with respect to a naturally defined class of short exact sequences called the ch-projective modules and ch-pure sequences, respectively. Every ${Z_p}$-module has a ch-pure projective resolution and every reduced ch-projective module is a summand of a SKT-module. It is finally shown that a ${Z_p}$-module M is ch-projective if and only if, for every ordinal $\alpha$, the two ${Z_p}$-modules ${p^\alpha }M$ and $M/{p^\alpha }M$ are both ch-projective.