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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
DOI: https://doi.org/10.1090/S0002-9939-1981-0619970-X
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.

References [Enhancements On Off] (What's this?)

  • [1] E. G. Effros, Dimensions and $ {C^* }$-algebras, Lecture Notes, UCLA, August, 1980.
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  • [3] E. G. Effros and C. L. Shen, Dimension groups and finite difference equations, J. Operator Theory 2 (1979), 215-231. MR 559606 (82k:46088)
  • [4] N. Riedel, Classification of dimension groups and iterating systems, Math. Scand. 48 (1981). MR 631337 (82k:46091)
  • [5] W. M. Schmidt, Diophantine approximation, Lecture Notes in Math., vol. 785, Springer-Verlag, Berlin and New York, 1980. MR 568710 (81j:10038)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0619970-X
Article copyright: © Copyright 1981 American Mathematical Society

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