Every finite abelian group is the Brauer group of a ring

Ford, T. J.

doi:10.1090/S0002-9939-1981-0612710-X

Every finite abelian group is the Brauer group of a ring
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by T. J. Ford PDF

Proc. Amer. Math. Soc. 82 (1981), 315-321 Request permission

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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