A Cancellation Criterion for Finite-Rank Torsion-Free Abelian Groups
Copyright policy )A Cancellation Criterion for Finite-Rank Torsion-Free Abelian Groups
In this paper, a necessary ring-theoretical criterion is given for a finite-rank torsion-free abelian group to have the cancellation property. This generalizes results obtained by L. Fuchs and F. Loonstra [5] for the rank-one case and resolves the cancellation problem for strongly indecomposable groups.
Torsion-free groups, finite rank, Direct sums, direct products, etc. for abelian groups, torsion-free abelian groups of finite rank, Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups, finitely generated abelian groups, unit of End(G), strongly indecomposable torsion-free abelian group, stable range, cancellation property, Abelian groups
Torsion-free groups, finite rank, Direct sums, direct products, etc. for abelian groups, torsion-free abelian groups of finite rank, Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups, finitely generated abelian groups, unit of End(G), strongly indecomposable torsion-free abelian group, stable range, cancellation property, Abelian groups
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