Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The Brauer-Wall group of a commutative ring

Author: Charles Small
Journal: Trans. Amer. Math. Soc. 156 (1971), 455-491
MSC: Primary 13.90
MathSciNet review: 0276218
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let k be a commutative ring (with 1). We work with k-algebras with a grading $\bmod \;2$, and with graded modules over such algebras. Using graded notions of tensor product, commutativity, and morphisms, we construct an abelian group ${\rm {BW}}(k)$ whose elements are suitable equivalence classes of Azumaya k-algebras. The consruction generalizes, and is patterned on, the definition of the Brauer group ${\rm {Br}}(k)$ given by Auslander and Goldman. ${\rm {Br}}(k)$ is in fact a subgroup of ${\rm {BW}}(k)$, and we describe the quotient as a group of graded quadratic extensions of k.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 13.90

Retrieve articles in all journals with MSC: 13.90

Additional Information

Keywords: Brauer group of a commutative ring, separable algebra, Azumaya algebra, graded algebra, Galois extension of commutative rings, quadratic extension of commutative rings
Article copyright: © Copyright 1971 American Mathematical Society