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Smooth PI algebras with finite divisor class group


Authors: A. Braun and C. R. Hajarnavis
Journal: Proc. Amer. Math. Soc. 139 (2011), 849-854
MSC (2010): Primary 16E65, 16H05, 16P50, 16R20
DOI: https://doi.org/10.1090/S0002-9939-2010-10547-6
Published electronically: August 13, 2010
MathSciNet review: 2745637
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Abstract: We have shown in an earlier paper that the divisor class group of the centre of a smooth PI algebra with trivial $ K_0$ is a torsion group of finite exponent. We show here that this group need not be finite even in the affine case. Our example is an Azumaya algebra of global dimension 2. We also provide a positive result in a special case.


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Additional Information

A. Braun
Affiliation: Department of Mathematics, University of Haifa, Haifa 31905, Israel
Email: abraun@math2.haifa.ac.il

C. R. Hajarnavis
Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, England
Email: crh@maths.warwick.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-2010-10547-6
Received by editor(s): June 1, 2009
Received by editor(s) in revised form: April 14, 2010
Published electronically: August 13, 2010
Communicated by: Martin Lorenz
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.