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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Metric completions of ordered groups
and $K_0$ of exchange rings


Author: E. Pardo
Journal: Trans. Amer. Math. Soc. 350 (1998), 913-933
MSC (1991): Primary 16D70, 19K14, 20K20; Secondary 16A50, 46L55
MathSciNet review: 1376552
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Abstract: We give a description of the closure of the natural affine continuous function representation of $K_0(R)$ for any exchange ring $R$. This goal is achieved by extending the results of Goodearl and Handelman, about metric completions of dimension groups, to a more general class of pre-ordered groups, which includes $K_0$ of exchange rings. As a consequence, the results about $K_0^+$ of regular rings, which the author gave in an earlier paper, can be extended to a wider class of rings, which includes $C^*$-algebras of real rank zero, among others. Also, the framework of pre-ordered groups developed here allows other potential applications.


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Additional Information

E. Pardo
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
Address at time of publication: Departamento de Matematics, Universidad de Cādiz, Aptdo. 40, 11510 Puerto Real (Cādiz), Spain
Email: enrique.pardo@uca.es

DOI: http://dx.doi.org/10.1090/S0002-9947-98-01744-9
PII: S 0002-9947(98)01744-9
Keywords: Exchange ring, asymptotic refinement group, refinement monoid
Received by editor(s): October 12, 1995
Additional Notes: Partially supported by DGICYT Grant PB-93-0900 and by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya. This paper is part of the author’s Ph.D.Thesis, written under the supervision of Professor P. Ara
Article copyright: © Copyright 1998 American Mathematical Society