A Cohomological Approach to the Brauer-Long Group and the Groups of Galois Extensions and Strongly Graded Rings

DOI10.2307/2001740zbMath0724.13003OpenAlexW4233635230MaRDI QIDQ5202283

Beattie, Margaret, Stefaan Caenepeel

Publication date: 1991

Full work available at URL: https://doi.org/10.2307/2001740

zbMATH Keywords

Galois extensionsgraded ringsétale cohomology groupsBrauer-Long group

Mathematics Subject Classification ID

Brauer groups of schemes (14F22) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Galois theory and commutative ring extensions (13B05)

Related Items (11)

Quadratic forms with values in invertible modules ⋮ Some invariants for equivalent \(G\)-algebras ⋮ The Brauer-Long group of \({\mathbb{Z}}/p^ t{\mathbb{Z}}\)-dimodule algebras ⋮ The picard group of a category of graded modules ⋮ The Brauer group of Yetter-Drinfel’d module algebras ⋮ A Note on Inner Actions of Hopf Algebras ⋮ Computing the Brauer-Long group of a Hopf algebra. II: The Skolem-Noether theory ⋮ Equivariant central simple graded algebras and the equivariant Brauer-Wall group. ⋮ Computing the Brauer-Long group of a Hopf algebra. I: The cohomological theory ⋮ A Brauer-Clifford-long group for the category of dyslectic \((S, H)\)-dimodule algebras ⋮ The Brauer group of some quasitriangular Hopf algebras.

Cites Work

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• The Brauer Group of Graded Azumaya Algebras. II: Graded Galois Extensions
• Generalized Clifford Algebras and Dimodule Algebras
• On the Brauer Group of Algebras Having a Grading and an Action
• Clifford Algebras and Spinor Norms Over a Commutative Ring
• Graded Brauer Groups.
• The Brauer-Wall Group of a Commutative Ring
• The Brauer Group of Graded Azumaya Algebras

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