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More on the Schur group of a commutative ring

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  • R. A. Mollin

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.

Suggested Citation

  • R. A. Mollin, 1985. "More on the Schur group of a commutative ring," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 8, pages 1-8, January.
    • Handle: RePEc:hin:jijmms:831047
    DOI: 10.1155/S0161171285000308
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