Galois-Azumaya Extensions and the Brauer-Galois Group of a Commutative Ring

Abstract

We attach to any commutative ring R a subgroup of the Brauer group of R, called the Brauer-Galois group of R. Its elements are the classes of the Azumaya R-algebras which can be represented, via Brauer equivalence, by a Galois extension of R. We compute this group for some particular commutative fields.

24 pages, to be published in Bull. Soc. Math. Belg. Simon Stevin