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

 

Simple $AH$-algebras of real rank zero


Author: Huaxin Lin
Journal: Proc. Amer. Math. Soc. 131 (2003), 3813-3819
MSC (2000): Primary 46L05, 46L35
Published electronically: March 25, 2003
MathSciNet review: 1999928
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Abstract: Let $A$ be a unital simple $AH$-algebra with real rank zero. It is shown that if $A$ satisfies a so-called fundamental comparison property, then $A$ has tracial topological rank zero. Combining some previous results, it is shown that a unital simple $AH$-algebra with real rank zero, stable rank one and weakly unperforated $K_0(A)$ must have slow dimension growth.


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Additional Information

Huaxin Lin
Affiliation: Department of Mathematics, East China Normal University, Shanghai, People’s Republic of China
Address at time of publication: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222
Email: hxlin@noether.uoregon.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06995-8
PII: S 0002-9939(03)06995-8
Keywords: $AH$-algebras, tracial topological rank zero
Received by editor(s): May 7, 2001
Received by editor(s) in revised form: July 16, 2002
Published electronically: March 25, 2003
Additional Notes: This research was partially supported by NSF grant DMS 009790
Communicated by: David R. Larson
Article copyright: © Copyright 2003 American Mathematical Society