[PDF] The Brauer group of a commutative ring - Semantic Scholar
WEBThe Brauer group of a commutative ring. M. Auslander, O. Goldman. Published 1 March 1960. Mathematics. Transactions of the American Mathematical Society. Introduction. This paper contains the foundations of a general theory of separable algebras over arbitrary commutative rings.
WEBTHE BRAUER GROUP OF A COMMUTATIVE RING BY MAURICE AUSLANDER AND OSCAR GOLDMAN(') Introduction. This paper contains the foundations of a general theory of separable algebras over arbitrary commutative rings. Of the various equiv-alent conditions for separability in the classical theory of algebras over a
WEBThe Brauer Group. The Brauer group of a field K may be defined to be the group of similarity classes of central simple algebras over K or, equivalently, the cohomology group. H2.Gal.Ksep=K/;Ksep/ D H2..SpecK/et;Gm/: Both of these definitions generalize to schemes, but they may give different groups. The first group, that of similarity classes ...
WEBTHE BRAUER GROUP OF A COMMUTATIVE RING BY MAURICE AUSLANDER AND OSCAR GOLDMAN(') Introduction. This paper contains the foundations of a general theory of separable algebras over arbitrary commutative rings. Of the various equiv-alent conditions for separability in the classical theory of algebras over a
WEBThe Brauer group Br(R) of a commutative ring was introduced by Aus lander and Goldman in their 1960 paper The Brauer Group of a Commuta tive Ring, building on earlier work of Azumaya. This group coincides with the "classical" Brauer group (cf. Chapter 4) in the case when R is a field.
The Brauer Group of a Commutative Ring | SpringerLink
WEBThe Brauer group Br(R) of a commutative ring was introduced by Auslander and Goldman in their 1960 paper The Brauer Group of a Commutative Ring, building on earlier work of Azumaya. This group coincides with the “classical” Brauer group (cf. Chapter 4) in the case when R is a field.
WEBThe Brauer group of a eld F, classifying central simple algebras over F, plays a critical role in class eld theory. The de nition was generalized by Auslander and Goldman [1] to the case of a commutative ring: the Brauer group of R consists of Morita equivalence classes of Azumaya algebras over R.
Brauer group in nLab - ncatlab.org
WEBJun 6, 2023 · The Brauer group of a ring R R is a torsion subgroup of the second etale cohomology group of Spec R Spec R with values in the multiplicative group 𝔾 m \mathbb{G}_m Br ( X ) ↪ H et 2 ( X , 𝔾 m ) .
WEBAbstract. An algebra is a vector space V over a eld k together with a k-bilinear product of vectors under which V is a ring. A certain class of algebras, called Brauer algebras - algebras which split over a nite Galois extension -appear in many sub elds of abstract algebra, including K-theory and class eld theory.
The Brauer Group of Commutative Rings - Semantic Scholar
WEBThis thesis describes algorithms that answer questions arising in ring and module theory by describing algorithms that determine whether M and N are isomorphic, and shows how to compute a set of generators of minimal cardinality for a given module.