  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.

Rings and Algebras;Algebraic Geometry