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
DOI:
https://doi.org/10.1090/S0002-9939-01-06246-3
Published electronically:
November 15, 2001
MathSciNet review:
1887006
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: The category of local torsion-free abelian groups of finite rank is known to have the cancellation and 
-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:
https://doi.org/10.1090/S0002-9939-01-06246-3
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
