The Henselization of a valued division algebra

DOI10.1016/0021-8693(89)90247-0zbMath0676.16017OpenAlexW2062282062MaRDI QIDQ1122642

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0021-8693(89)90247-0

zbMATH Keywords

extensions ramification index valuations division algebras residue class rings valued fields Henselizations defectless residue degrees tensor products of valued division rings value groups

Mathematics Subject Classification ID

Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Infinite-dimensional and general division rings (16K40) Skew fields, division rings (12E15) Valued fields (12J10) General valuation theory for fields (12J20)

Related Items

Hasse principle for hermitian spaces over semi-global fields, Nontriviality of certain quotients of \(K_1\) groups of division algebras., An Involutorial Version of a Theorem of Gräter, Kummer subfields of tame division algebras, Nondegenerate Semiramified Valued and Graded Division Algebras, Graded Hermitian forms and Springer's theorem, Division algebra subfields introduced by an indeterminate, Dubrovin valuation rings and Henselization, Okubo algebras and valuations, On Brauer \(p\)-dimensions and absolute Brauer \(p\)-dimensions of Henselian fields, Value functions on simple Artinian rings, The corestriction of central simple algebras with dubrovin valuation rings, Indecomposable division algebras with a baer ordering, Signatures of Hermitian forms and ``prime ideals of Witt groups, A symmetric version of the notion of c-ordering, On Brauer \(p\)-dimensions and index-exponent relations over finitely-generated field extensions., Le gradué d’une algèbre à division valuée, Field of iterated Laurent series and its Brauer group, Asymptotic Brauer 𝑝-dimension, Galois subfields of inertially split division algebras., \(\text{SK}_1\) of graded division algebras., Valuations on algebras with involution., Baer orderings with noninvariant valuation ring, On decomposing c-valued division rings, On the tensor product of division algebras, Forms and Baer ordered *-fields, Central Extensions of n-Ordered Division Rings, On the non-existence of cyclic splitting fields for division algebras, Prime to \(p\) extensions of the generic Abelian crossed product., The Joly-Becker theorem for \(*\)-orderings, On the behaviour of Brauer \(p\)-dimensions under finitely-generated field extensions., A Valuation Theory for Nonassociative Quaternion Algebras, A Hermitian analogue of the Bröcker-Prestel theorem., Value Functions on Central Simple Algebras, Value functions and associated graded rings for semisimple algebras, Value functions and Dubrovin valuation rings on simple algebras, Integral Dubrovin Valuation Rings, Division algebras over Henselian fields., Central extensions of \(*\)-ordered skew fields, On the Dec group of finite abelian Galois extensions over global fields, Trees and valuation rings, On the First Galois Cohomology Group of the Algebraic Group SL₁(D), Bicyclic algebras of prime exponent over function fields, Prime to \(p\) extensions of division algebras, Correspondences between valued division algebras and graded division algebras, Subfields of Nondegenerate Tame Semiramified Division Algebras, Strongly Anisotropic Involutions on Central Simple Algebras, Linkage of symbol \(p\)-algebras of degree 3, Period and index in the Brauer group of an arithmetic surface, Co-Henselian extensions and Henselizations of skew fields, Rings of the Morita Contexts and Semihereditary MaximalV-Orders, Residually *-Abelian Valuation, Valuations on tensor powers of a division algebra., Decomposing and ordering a certain crossed product, On the \(u\)-invariant for quadratic forms and the linkage of cyclic algebras, Central extensions of ordered skew fields

Cites Work