More on the Schur group of a commutative ring
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1985-01-01
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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.
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R. A. Mollin, “More on the Schur group of a commutative ring,” International Journal of Mathematics and Mathematical Sciences, vol. 8, no. 3, pp. 513-520, 1985. doi:10.1155/S0161171285000552