On torsion-free periodic rings.
An exact sequence of torsion-free abelian groups is quasi-balanced if the induced sequence is exact for all rank-1 torsion-free abelian groups . This paper sets forth the basic theory of quasi-balanced sequences, with particular attention given to the case in which is a Butler group. The special case where is almost completely decomposable gives rise to a descending chain of classes of Butler groups. This chain is a generalization of the chain of Kravchenko classes that arise from balanced...
Let G be an abelian group and ◻ G its square subgroup as defined in the introduction. We show that the square subgroup of a non-homogeneous and indecomposable torsion-free group G of rank two is a pure subgroup of G and that G/◻ G is a nil group.