International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1985 / Article

Open Access

Volume 8 |Article ID 831047 | https://doi.org/10.1155/S0161171285000308

R. A. Mollin, "More on the Schur group of a commutative ring", International Journal of Mathematics and Mathematical Sciences, vol. 8, Article ID 831047, 8 pages, 1985. https://doi.org/10.1155/S0161171285000308

More on the Schur group of a commutative ring

Received10 Jul 1984

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 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.

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.


More related articles

 PDF Download Citation Citation
 Order printed copiesOrder
Views67
Downloads209
Citations

Related articles

We are committed to sharing findings related to COVID-19 as quickly as possible. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. Review articles are excluded from this waiver policy. Sign up here as a reviewer to help fast-track new submissions.