Pi-balanced torsion-free modules over a discrete valuation domain

Pi-balanced images of a finite direct sum L=J1 Jn of purely indecomposable modules over a discrete valuation domain are investigated. Under a rigidity condition, these images can be classified by a complete set of isomorphism invariants. When the Ji have finite rank, the torsion-free images of L admit an internal characterization. If, in addition, the Ji are all isomorphic, then any pi-balanced image of L is a direct summand. Several examples illustrate the concepts and the results.