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

 

Refinement monoids with weak comparability
and applications to regular rings
and $C^*$-algebras


Authors: P. Ara and E. Pardo
Journal: Proc. Amer. Math. Soc. 124 (1996), 715-720
MSC (1991): Primary 16E20, 16E50, 46L80, 19K14, 06F20
MathSciNet review: 1301484
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove a cancellation theorem for simple refinement monoids satisfying the weak comparability condition, first introduced by K.C. O'Meara in the context of von Neumann regular rings. This result is then applied to von Neumann regular rings and $C^*$-algebras of real rank zero via the monoid of isomorphism classes of finitely generated projective modules.


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Additional Information

P. Ara
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bella- terra (Barcelona), Spain
Email: para@mat.uab.es

E. Pardo
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bella- terra (Barcelona), Spain; Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bella- terra (Barcelona), Spain
Email: epardo@mat.uab.es

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03059-6
PII: S 0002-9939(96)03059-6
Keywords: Refinement monoid, $C^*$-algebra with real rank zero, von Neumann regular ring, weak comparability
Received by editor(s): May 19, 1994
Received by editor(s) in revised form: September 21, 1994
Additional Notes: The research of the authors was supported by grants from the DGICYT (Spain).
Dedicated: Dedicat al petit Guillem
Communicated by: Ken Goodearl
Article copyright: © Copyright 1996 American Mathematical Society