Normality of algebras over commutative rings and the Teichmüller class. I: The absolute case

DOI10.1007/s40062-017-0173-3zbMath1439.13025OpenAlexW2999097549MaRDI QIDQ1744181

Johannes Huebschmann

Publication date: 16 April 2018

Published in: Journal of Homotopy and Related Structures (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40062-017-0173-3

zbMATH Keywords

Galois cohomologyAzumaya algebracrossed productBrauer groupcrossed modulenon-abelian cohomologynon-commutative Galois theorynormal algebracrossed pairDeuring embedding problemGalois theory of commutative ringsGroup cohomologyTeichmüller cocycle

Mathematics Subject Classification ID

Galois cohomology (12G05) Cohomology of groups (20J06) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Twisted and skew group rings, crossed products (16S35) Brauer groups (algebraic aspects) (16K50) Galois theory and commutative ring extensions (13B05)

Related Items (4)

Normality of algebras over commutative rings and the Teichmüller class. I: The absolute case ⋮ Normality of algebras over commutative rings and the Teichmüller class. II: Crossed pairs and the relative case ⋮ Normality of algebras over commutative rings and the Teichmüller class. III: Examples ⋮ On the history of Lie brackets, crossed modules, and Lie-Rinehart algebras

Cites Work

• Nonabelian algebraic topology. Filtered spaces, crossed complexes, cubical homotopy groupoids. With contributions by Christopher D. Wensley and Sergei V. Soloviev
• Principal homogeneous spaces for arbitrary Hopf algebras
• On the Teichmüller cocycle map
• An interpretation of the cohomology groups \(H^ n(G,M)\)
• Automorphisms of group extensions and differentials in the Lyndon-Hochschild-Serre spectral sequence
• Crossed \(n\)-fold extensions of groups and cohomology
• Affine Quotientenschemata nach affinen, algebraischen Gruppen und induzierte Darstellungen
• Brauer groups and Amitsur cohomology for general commutative ring extensions
• Graded extensions of categories
• Normality of algebras over commutative rings and the Teichmüller class. I: The absolute case
• Normality of algebras over commutative rings and the Teichmüller class. II: Crossed pairs and the relative case
• On commutor rings and Galois theory of separable algebras
• The Brauer group of a ringed space
• Hopf algebras and Galois theory
• On normal Azumaya algebras and the Teichmüller cocycle map
• Automorphisms of separable algebras
• Über normale, zentrale, separable Algebren und Amitsur-Kohomologie
• On a 3-cohomology class in class field theory and the relationship of algebra- and idèle-classes
• On Ramification Theory in Noetherian Rings
• The Brauer Group of a Commutative Ring
• Group extensions, crossed pairs and an eight term exact sequence.
• Maximal Orders
• Cohomology and Galois Theory. I. Normality of Algebras and Teichmuller's Cocycle
• A nonassociative method for associative algebras
• Symmetry of algebras over a number field
• Combinatorial homotopy. II
• Cohomology of Group Extensions
• Compound Group Extensions. I. Continuations of Normal Homomorphisms
• Graded extensions of monoidal categories
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