Balanced projective and cobalanced injective torsion free groups of finite rank (Q1076811)

Let TF denote the category of torsion free abelian groups of finite rank and homomorphisms. The authors prove that a group A in TF is completely indecomposable if and only if A is projective with respect to all balanced exact sequences in TF if and only if A is injective with respect to all co-balanced exact sequences in TF. Using different techniques, the authors obtained similar results in [Abelian group theory, Lect. Notes Math. 1006, 144-163 (1983; Zbl 0525.20036)].