AbstractLetE(G)=End(G)/N(End(G)). Our goal in this paper is to study direct sum decompositions of certain reduced torsion-free finite rank (rtffr) abelian groups by introducing an ideal τ of E(G) called a conductor of G. This ideal induces a natural ring decomposition E(G)=E(G)(τ)×E(G)τ and a natural direct sum decomposition G=G(τ)⊕Gτ for an rtffr group G.Let {G1,…,Gt} be a set of strongly indecomposable rtffr groups such that Gi≇˙Gj for each i≠j∈{1,…,t}, and such that E(Gi) is a Dedekind domain for each i∈{1,…,t}. Let n1,…,nt>0 be integers and letG¯=G1n1⊕⋯⊕Gtnt. We say that G has semi-primary index in G¯ if for each i=1,…,t there is a primary ideal Pi⊂End(Gi) such thatP1G1n1⊕⋯⊕PtGtnt⊂G⊂G¯. The group G is balanced in G¯ if G⊂G¯ and if E(G)⊂E(G¯). We say that G is a balanced semi-primary group if there is a balanced embedding G⊂G¯ such that G has semi-primary index in G¯. TheoremIf G is a balanced semi-primary rtffr group then G has a locally unique decomposition and the local refinement property.