Bulletin of the Belgian Mathematical Society - Simon Stevin

Galois-Azumaya extensions and the Brauer-Galois group of a commutative ring

Philippe Nuss

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Abstract

For any commutative ring $R$, we introduce a group attached to $R$, the {\em Brauer-Galois group of $R$}, defined to be the subgroup of the Brauer group of $R$ consisting of 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 rings.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 13, Number 2 (2006), 247-270.

Dates
First available in Project Euclid: 19 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1148059461

Digital Object Identifier
doi:10.36045/bbms/1148059461

Mathematical Reviews number (MathSciNet)
MR2259905

Zentralblatt MATH identifier
1135.16021

Subjects
Primary: 16H05: Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) 16K50: Brauer groups [See also 12G05, 14F22] 19C30: $K_2$ and the Brauer group 16W22: Actions of groups and semigroups; invariant theory
Secondary: 16W20: Automorphisms and endomorphisms

Keywords
noncommutative ring Galois-extension Azumaya algebra quaternion Brauer group

Citation

Nuss, Philippe. Galois-Azumaya extensions and the Brauer-Galois group of a commutative ring. Bull. Belg. Math. Soc. Simon Stevin 13 (2006), no. 2, 247--270. doi:10.36045/bbms/1148059461. https://projecteuclid.org/euclid.bbms/1148059461


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