A projective characterization for SKT-modules

Abstract

In this paper a class of abelian groups (SKT-modules), which includes the torsion totally projective groups, 5-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 Zp-module has a ch-pure projective resolution and every reduced ch-projective module is a summand of a SKT-module. It is finally shown mat a Zp-module M is ch-projective if and only if, for every ordinal a, the two Z.-modules p"M and M/p"M are both ch-projective. 1. Definitions. If p is a prime number then the ring of all rational numbers a/b with b relatively prime top will be denoted by Zp.

The calculation of an invariant for Tor

“…In [7], it was shown that the S-groups are the /?-groups protective relative to a class of short exact sequences. Since the class of ^-groups has a protective characterization and contains the totally protective /^-groups, and since each totally protective /7-group is /?…”

A classification theorem for SKT-modules

“…These groups are called SKT-modules. It will be shown in [4] that SKT-modules are projective relative to a well-defined class of sequences. It then follows that the SKT-modules form a class of groups which contains the 5-groups and balanced projectives, have a projective characterization, and a complete family of invariants.…”