Indecomposable decompositions of torsion-free abelian groups

Abstract

An indecomposable decomposition of a torsion-free abelian group G of rank n is a decomposition G = A 1 ⊕ · · · ⊕ At where each A i is indecomposable of rank r i , so that i r i = n is a partition of n. The group G may have indecomposable decompositions that result in different partitions of n. We address the problem of characterizing those sets of partitions of n which can arise from indecomposable decompositions of a torsion-free abelian group.2010 Mathematics Subject Classification. 20K15, 20K25.