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Mathematics of the USSR-Izvestiya, 1985, Volume 25, Issue 3, Pages 573–599
DOI: https://doi.org/10.1070/IM1985v025n03ABEH001308 (Mi im1518) 		 
This article is cited in 6 scientific papers (total in 7 papers)

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

V. P. Platonov, V. I. Yanchevskii
English version PDF (1524 kB) Citations (7) Russian version article
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DOI: https://doi.org/10.1070/IM1985v025n03ABEH001308
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.
Received: 30.05.1984
Bibliographic databases:
UDC: 512.74+512.552
MSC: 20G15, 12E15, 13A39, 16A54
Language: English
Original paper language: Russian
Citation: V. P. Platonov, V. I. Yanchevskii, “Dieudonné's conjecture on the structure of unitary groups over a division ring, and Hermitian $K$-theory”, Math. USSR-Izv., 25:3 (1985), 573–599
Citation in format AMSBIB
\Bibitem{PlaYan84}
\by V.~P.~Platonov, V.~I.~Yanchevskii
\paper Dieudonn\'e's conjecture on the structure of unitary groups over a~division ring, and Hermitian $K$-theory
\jour Math. USSR-Izv.
\yr 1985
\vol 25
\issue 3
\pages 573--599
\mathnet{http://mi.mathnet.ru//eng/im1518}
\crossref{https://doi.org/10.1070/IM1985v025n03ABEH001308}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=772116}
\zmath{https://zbmath.org/?q=an:0593.16012|0579.16011}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
     
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