This article is cited in 6 papers

Dieudonné's conjecture on the structure of unitary groups over a division ring, and Hermitian $K$-theory

V. P. Platonov, V. I. Yanchevskii


Abstract: A multiplicative theory of finite-dimensional division rings with involutions of the first kind is developed in connection with Dieudonné's conjecture, and the structure of arbitrary division rings over Henselian fields is studied. The unitary Whitehead group $UK_1(\tau,A)$ is computed for Henselian division rings $A$ with an involution $\tau$. Classes of division rings for which Dieudonné's conjecture has an affirmative answer are exhibited.
Bibliography: 17 titles.

UDC: 512.74+512.552

MSC: 20G15, 12E15, 13A39, 16A54

Received: 30.05.1984

 English version: Mathematics of the USSR-Izvestiya, 1985, 25:3, 573–599

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