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
The Schur group of a commutative ring, , with identity consists of all classes in the Brauer group of which contain a homomorphic image of a group ring for some finite group . 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.
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