Extending Valuations to Finite Dimensional Division Algebras

DOI10.2307/2045758zbMath0601.12028OpenAlexW4252146173MaRDI QIDQ3735823

Adrian R. Wadsworth

Publication date: 1986

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

Full work available at URL: https://doi.org/10.2307/2045758

zbMATH Keywords

non-commutative valuation theoryextension of valuationsfinite dimensional division algebras

Mathematics Subject Classification ID

Finite-dimensional division rings (16K20) Skew fields, division rings (12E15) General valuation theory for fields (12J20)

Related Items (37)

A Springer theorem for Hermitian forms. ⋮ Hasse principle for hermitian spaces over semi-global fields ⋮ Nontriviality of certain quotients of \(K_1\) groups of division algebras. ⋮ Extensions of Valuation Rings in Central Simple Algebras ⋮ Totally Ramified Valuations on Finite-Dimensional Division Algebras ⋮ On torsion subgroups of Whitehead groups of division algebras. ⋮ Weakly *-ordered *-fields ⋮ Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable ⋮ Graded Hermitian forms and Springer's theorem ⋮ Dubrovin valuation rings and Henselization ⋮ Okubo algebras and valuations ⋮ Valuation rings in finite-dimensional division algebras ⋮ Correction to a theorem on c-ordering ⋮ The Henselization of a valued division algebra ⋮ Algebraic elements in division rings ⋮ \(G\)-valuations and \(G\)-valuation rings ⋮ \(\text{SK}_1\) of graded division algebras. ⋮ Valuations on algebras with involution. ⋮ Baer orderings with noninvariant valuation ring ⋮ On decomposing c-valued division rings ⋮ Pythagorean \(*\)-fields ⋮ Galois cohomology and forms of algebras over Laurent polynomial rings ⋮ A note on the special unitary group of a division algebra ⋮ On the residue fields of Henselian valued stable fields ⋮ Maximal orders over valuation rings ⋮ A note on valued division algebras ⋮ Wedderburn’s factorization theorem application to reduced $K$-theory ⋮ Noncrossed Product Division Algebras with a Baer Ordering ⋮ Valuations on Algebraic Division Algebras ⋮ Value functions and associated graded rings for semisimple algebras ⋮ Division algebras over Henselian fields. ⋮ On extending Prüfer rings in central simple algebras ⋮ Correspondences between valued division algebras and graded division algebras ⋮ Henselian valued stable fields ⋮ The genus of a division algebra and the unramified Brauer group ⋮ Valuations on tensor powers of a division algebra. ⋮ Hermitian 𝑢-invariants over function fields of 𝑝-adic curves

This page was built for publication: Extending Valuations to Finite Dimensional Division Algebras