Metric completions of ordered groups and 𝐾₀ of exchange rings

Pardo, E.

doi:10.1090/S0002-9947-98-01744-9

Metric completions of ordered groups and $K_0$ of exchange rings
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by E. Pardo

Trans. Amer. Math. Soc. 350 (1998), 913-933

DOI: https://doi.org/10.1090/S0002-9947-98-01744-9

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