More on the Schur group of a commutative ring. (1985)

• Record Type: Journal Article
• Authors: Mollin, R. A.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 8:Number 2(1985)
• Page Start: 275
• Page End: 282
• Publication Date: 1985
• Subjects: Schur index -- group ring -- automorphism; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171285000308
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : The Schur group of a commutative ring, R, with identity consists of all classes in the Brauer group ofR which contain a homomorphic image of a group ringR G for some finite groupG . 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.