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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The connected stable rank of the purely infinite simple $C^*$-algebras
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by Yifeng Xue PDF
Proc. Amer. Math. Soc. 127 (1999), 3671-3676 Request permission

Abstract:

Suppose that $\mathcal A$ is a unital purely infinite simple $C^*$-algebra. If the class [1] of the unit 1 in $K_0(\mathcal A)$ has torsion, then $\operatorname {csr}(\mathcal A)=\infty$; if [1] is torsion-free in $K_0(\mathcal A)$, then $\operatorname {csr}(\mathcal A)=2$. If $\mathcal A$ is a non-unital purely infinite simple $C^*$-algebra, then $\operatorname {csr}(\mathcal A)=2$.
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Additional Information
  • Yifeng Xue
  • Affiliation: Institute of Fundamental Education, East China University of Science and Technology, Shanghai 200237, People’s Republic of China
  • Address at time of publication: Department of Mathematics, East China University of Science and Technology, Shanghai 200237, People’s Republic of China
  • Received by editor(s): August 1, 1997
  • Received by editor(s) in revised form: February 24, 1998
  • Published electronically: July 12, 1999
  • Communicated by: David R. Larson
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 3671-3676
  • MSC (1991): Primary 46L05
  • DOI: https://doi.org/10.1090/S0002-9939-99-05397-6
  • MathSciNet review: 1670439