Produits croises Abeliens

DOI10.1016/0021-8693(81)90227-1zbMath0473.16004OpenAlexW1998888137MaRDI QIDQ1158490

Jean-Pierre E. Tignol

Publication date: 1981

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(81)90227-1

zbMATH Keywords

cyclic algebrasrelative Brauer groupsgeneric abelian crossed productsskewfields with involution

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Grothendieck groups, (K)-theory, etc. (16E20) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Brauer groups of schemes (14F22) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Homological methods in associative algebras (16Exx) Division rings and semisimple Artin rings (16Kxx)

Related Items (16)

Cyclic and elementary abelian subfields of Malcev-Neumann division algebras ⋮ Produits croisés mixtes: extensions de groupes et extensions d'anneaux ⋮ Kummer subfields of tame division algebras ⋮ Nondegenerate Semiramified Valued and Graded Division Algebras ⋮ Indecomposable algebras of prime exponent. ⋮ Triple Massey products vanish over all fields ⋮ \(\text{SK}_1\) of graded division algebras. ⋮ On decomposing c-valued division rings ⋮ Unitary \(\mathrm{SK}_1\) of semiramified graded and valued division algebras. ⋮ Degeneracy and decomposability in Abelian crossed products. ⋮ Division algebras over Henselian fields. ⋮ On the Dec group of finite abelian Galois extensions over global fields ⋮ Subfields of Nondegenerate Tame Semiramified Division Algebras ⋮ Similarity of quadratic forms and half-neighbors ⋮ Kummer subfields of Malcev-Neumann division algebras ⋮ The second trace form of a central simple algebra of degree 4 of characteristic 2.

Cites Work

• Prime spectra in non-commutative algebra
• Cohomologische Invarianten quadratischer Formen
• Generic Abelian crossed products and \(p\)-algebras
• Central simple algebras
• Generic construction of non-cyclic division algebras
• Corps a Involution Neutralises par une Extension Abelienne Elementaire
• SK1 von Algebren über vollständig diskret bewerteten Körpern und Galoiskohomologie abelscher Körpererweiterungen.
• Division algebras of degree 4 and 8 with involution
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