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

2005/01/17 by Philippe Nuss, Nuss, Philippe
Mathematics · #16H05 #16K50 #16W22 (Primary) 16W20 (Secondary) #19C30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Rings and Algebras (math.RA) #math.AG #math.RA #msc:16H05 #msc:16K50 #msc:16W20 #msc:16W22 #msc:19C30

paper · pdf · doi:10.48550/arxiv.math/0501254

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

arxiv created 2005/01/17 · arxiv updated 2009/12/01

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.

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