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

 

A counterexample to the unimodular conjecture on finitely generated dimension groups


Author: Norbert Riedel
Journal: Proc. Amer. Math. Soc. 83 (1981), 11-15
MSC: Primary 06F20; Secondary 10F10, 46L99
MathSciNet review: 619970
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Abstract: We give a series of examples of simple finitely generated dimension groups which cannot be obtained as the inductive limit of a system

$\displaystyle {{\mathbf{Z}}^r}\mathop \to \limits^{{A_1}} {{\mathbf{Z}}^r}\mathop \to \limits^{{A_2}} \cdots {{\mathbf{Z}}^r}\mathop \to \limits^{{A_n}} \cdots ,$

where each $ A_{n}$ is a unimodular matrix whose entries are nonnegative integers.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0619970-X
PII: S 0002-9939(1981)0619970-X
Article copyright: © Copyright 1981 American Mathematical Society