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International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 3, Pages 513-520
http://dx.doi.org/10.1155/S0161171285000552

More on the Schur group of a commutative ring

Mathematics Department, University of Calgary, Calgary, Alberta T2N 1N4, Canada

Received 10 July 1984

Copyright © 1985 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The Schur group of a commutative ring, R, with identity consists of all classes in the Brauer group of R which contain a homomorphic image of a group ring RG for some finite group G. It is the purpose of this article to continue an investigation of this group which was introduced in earler work as a natural generalization of the Schur group of a field. We generalize certain facts pertaining to the latter, among which are results on extensions of automorphisms and decomposition of central simple algebras into a product of cyclics. Finally we introduce the Schur exponent of a ring which equals the well-known Schur index in the global or local field case.