Smooth pi algebras with finite divisor class group

A. Braun; C. R. Hajarnavis

doi:10.1090/S0002-9939-2010-10547-6

Smooth pi algebras with finite divisor class group

A. Braun, C. R. Hajarnavis

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We have shown in an earlier paper that the divisor class group of the centre of a smooth PI algebra with trivial K₀ 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.

Original language	English
Pages (from-to)	849-854
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	139
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-2010-10547-6
State	Published - Mar 2011

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-2010-10547-6

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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 K0 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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AB - We have shown in an earlier paper that the divisor class group of the centre of a smooth PI algebra with trivial K0 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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Smooth pi algebras with finite divisor class group

Abstract

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