Direct sums of local torsion-free abelian groups
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- by David M. Arnold PDF
- Proc. Amer. Math. Soc. 130 (2002), 1611-1617 Request permission
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.References
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Additional Information
- David M. Arnold
- Affiliation: Department of Mathematics, Baylor University, Waco, Texas 76798-7328
- Email: David_Arnold@baylor.edu
- 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
- © Copyright 2001 American Mathematical Society
- 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
- MathSciNet review: 1887006