International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 2, Pages 275-282

More on the Schur group of a commutative ring

R. A. Mollin

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

Received 10 July 1984

Copyright © 1985 R. A. Mollin. 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.


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 earlier 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.