Direct sums of local torsion-free abelian groups-Reference-Cited by-同舟云学术

Direct sums of local torsion-free abelian groups

Published:2001-11-15 Issue:6 Volume:130 Page:1611-1617
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Arnold David

Abstract

The category of local torsion-free abelian groups of finite rank is known to have the cancellation and n 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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2002-130-06/S0002-9939-01-06246-3/S0002-9939-01-06246-3.pdf

Reference12 articles.

1. [Arnold 72] Arnold, D. A duality for torsion-free modules of finite rank over a discrete valuation ring, Proc. Lond. Math. Soc. (3) 24 (1972), 204-216.

2. Lecture Notes in Mathematics;Arnold, David M.,1982

3. CMS Books in Mathematics/Ouvrages de Math\'{e}matiques de la SMC;Arnold, David M.,2000

4. [Arnold 01] Arnold, D. Direct sum decompositions of torsion-free abelian groups of finite rank, Abelian Groups, Rings, and Modules (Proc. of 2000 Perth Conf.), Cont. Math., AMS, Providence, Rhode Island, 2001, 65-74.

5. [Arnold Dugas 00] Arnold, D. and Dugas, M. Co-purely indecomposable modules over a discrete valuation ring, J. Pure and Appl. Alg. 161 (2001), 1-12.

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Modules over Discrete Valuation Domains. III;Journal of Mathematical Sciences;2021-09-22

2. Modules over discrete valuation domains. II;Journal of Mathematical Sciences;2008-06

3. Modules over discrete valuation domains. I;Journal of Mathematical Sciences;2007-09

4. Pure Submodules of Finite Direct Sums of Co-Purely Indecomposable Modules;Communications in Algebra;2006-12-26

5. Torsion-free modules of finite rank over a discrete valuation ring;Journal of Algebra;2004-02