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

 

Every finite abelian group is the Brauer group of a ring


Author: T. J. Ford
Journal: Proc. Amer. Math. Soc. 82 (1981), 315-321
MSC: Primary 13A20
MathSciNet review: 612710
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Abstract: Given an arbitrary finite abelian group $ G$ a ring $ R$ is constructed using cohomological techniques from algebraic geometry whose Brauer group is $ G$. If $ G$ is a cyclic group, then $ R$ can be taken to be a three-dimensional noetherian integral domain. If $ G$ is not a cyclic group the ring $ R$ is a three-dimensional noetherian ring. At the expense of raising the dimension of $ R$, $ R$ can be chosen to be a domain. We also calculate $ B(R[x,1/x])$ for $ R$ a commutative noetherian regular ring containing a field of characteristic zero.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0612710-X
PII: S 0002-9939(1981)0612710-X
Article copyright: © Copyright 1981 American Mathematical Society