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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Direct sums of local torsion-free abelian groups


Author: David M. Arnold
Journal: Proc. Amer. Math. Soc. 130 (2002), 1611-1617
MSC (2000): Primary 20K15, 20K25
Published electronically: November 15, 2001
MathSciNet review: 1887006
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Abstract: The category of local torsion-free abelian groups of finite rank is known to have the cancellation and $n$-th root properties but not the Krull-Schmidt property. It is shown that 10 is the least rank of a local torsion-free abelian group with two non-equivalent direct sum decompositions into indecomposable summands. This answers a question posed by M.C.R. Butler in the 1960's.


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Additional Information

David M. Arnold
Affiliation: Department of Mathematics, Baylor University, Waco, Texas 76798-7328
Email: David_Arnold@baylor.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06246-3
PII: S 0002-9939(01)06246-3
Keywords: Krull-Schmidt groups, direct sum decompositions, local torsion-free abelian groups
Received by editor(s): October 4, 2000
Received by editor(s) in revised form: January 8, 2001
Published electronically: November 15, 2001
Additional Notes: This research was supported, in part, by the Baylor University Summer Sabbatical Program
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2001 American Mathematical Society