The quasi-Baer-splitting property for mixed abelian groups

The quasi-Baer-splitting property is extended from self-small torsion free groups to arbitrary self-small abelian groups. The self-small group A has this property iff it is almost-faithful as an E-module. This fact is reflected in the structure of A/t(A) as a module over the Walk-endomorphism ring of A. A self-small group A is almost E-flat and has the quasi-Baer-splitting property iff the class of almost A-adstatic modules is closed with respect to submodules and iff A is “almost-projective” with respect to the class of almost A-static groups.