Value functions and associated graded rings for semisimple algebras

DOI10.1090/S0002-9947-09-04681-9zbMath1195.16043OpenAlexW1979541460MaRDI QIDQ5189148

Adrian R. Wadsworth, Jean-Pierre E. Tignol

Publication date: 8 March 2010

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-09-04681-9

zbMATH Keywords

central simple algebrasnormsfinite-dimensional division algebrasHenselian fieldsassociated graded ringsgraded Brauer groupsMorandi value functionssurmultiplicative value functionstame gauges

Mathematics Subject Classification ID

Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Finite-dimensional division rings (16K20) Brauer groups (algebraic aspects) (16K50) Valued fields (12J10) Filtered associative rings; filtrational and graded techniques (16W70)

Related Items (18)

Galois subfields of tame division algebras. ⋮ Quasi-valuations extending a valuation ⋮ Algebras with involution that become hyperbolic over the function field of a conic. ⋮ Discriminants of symplectic graded involutions on graded simple algebras. ⋮ Domain theory aspects of extensions of integral domains ⋮ \(\text{SK}_1\) of graded division algebras. ⋮ Valuations on algebras with involution. ⋮ Discriminants of orthogonal involutions on central simple algebras with tame gauges. ⋮ Springer's theorem for tame quadratic forms over Henselian fields ⋮ Norms and gauges on Clifford Algebra ⋮ ON GENERALIZED GRADED CROSSED PRODUCTS AND KUMMER SUBFIELDS OF SIMPLE ALGEBRAS ⋮ A Note onK-Theory of Azumaya Algebras ⋮ Unitary \(\mathrm{SK}_1\) of semiramified graded and valued division algebras. ⋮ Value functions and Dubrovin valuation rings on simple algebras ⋮ On the Dec group of finite abelian Galois extensions over global fields ⋮ Extensions of integral domains and quasi-valuations ⋮ Strongly Anisotropic Involutions on Central Simple Algebras ⋮ Quasi-valuations and algebras over valuation domains

Cites Work

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• Division algebras over Henselian fields.
• Dubrovin valuation rings and Henselization
• The Henselization of a valued division algebra
• Prime ideals in PI-rings
• Non-commutative valuation rings and semi-hereditary orders
• Correspondences between valued division algebras and graded division algebras
• Théorie de la descente et algèbres d'Azumaya
• Graded Hermitian forms and Springer's theorem
• Totally Ramified Valuations on Finite-Dimensional Division Algebras
• Value Functions on Central Simple Algebras
• Integral Dubrovin Valuation Rings
• Schémas en groupes et immeubles des groupes classiques sur un corps local
• Extending Valuations to Finite Dimensional Division Algebras
• The Defektsatz for Central Simple Algebras
• Algebraic extensions of graded and valued fields
• Le gradué d’une algèbre à division valuée
• Valued Fields

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