Triviality of the Functor Coker(K 1(F) → K 1(D)) for Division Algebras

DOI10.1081/AGB-200060525zbMath1089.16014MaRDI QIDQ5462863

Uzi Vishne, Roozbeh Hazrat

Publication date: 27 July 2005

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

zbMATH Keywords

division algebrasEuclidean fieldscyclic algebrassimple algebrasreal Pythagorean fields

Mathematics Subject Classification ID

Grothendieck groups, (K)-theory, etc. (16E20) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Whitehead groups and (K_1) (19B99) Finite-dimensional division rings (16K20)

Related Items (5)

Nontriviality of certain quotients of \(K_1\) groups of division algebras. ⋮ Reduced \(K\)-theory of Azumaya algebras. ⋮ UNIT GROUPS OF CENTRAL SIMPLE ALGEBRAS AND THEIR FRATTINI SUBGROUPS ⋮ On maximal subgroups of the multiplicative group of a division algebra. ⋮ A Decomposition Theorem for CK₁of Central Simple Algebras

Cites Work

• Division rings and the square root of -1
• On the simplicity of the multiplicative group of an existentially closed skew field
• Finite-Dimensional Division Algebras over Fields
• On the Commutator Group of a Simple Algebra
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