More on the Schur group of a commutative ring

R. A. Mollin

International Journal of Mathematics and Mathematical Sciences, 1985, vol. 8, 1-8

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 R G 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.

Date: 1985
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:831047

DOI: 10.1155/S0161171285000308

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