First we introduce the concept of QD-hulls in arbitrary abelian groups. Then we use the concept to give a new characterization of purifiable torsion-free finite rank subgroups of an arbitrary abelian group. Finally we use it to formulate a splitting criterion for mixed groups of torsion-free finite rank.
"Splitting mixed groups of torsion-free finite rank II." Hokkaido Math. J. 42 (3) 331 - 343, February 2013. https://doi.org/10.14492/hokmj/1384273385