RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb. (N.S.), 1976, Volume 100(142), Number 2(6), Pages 191–200 (Mi msb2869)  

This article is cited in 7 scientific papers (total in 8 papers)

The infinitude of the reduced Whitehead group in the Tannaka–Artin problem

V. P. Platonov


Abstract: Using the methods and results of preceding papers of the author (V. P. Platonov, The Tarmaka–Artin problem and groups of projective conorms, Dokl. Akad. Nauk SSSR, 222, № 6 (1975), 1229–1302; The Tarmaka–Artin problem and reduced $K$-theory, Izv. Akad. Nauk SSSR, Ser. Mat., 40, № 2 (1976), 227–261), in the first part of this paper we find conditions under which the reduced Whitehead group is infinite, and in the second, larger part we give the solution of the Tannaka–Artin problem for cyclic algebras. In particular, we completely calculate the reduced Whitehead group $SK_1(A)$ for cyclic algebras $A$ over formal power series fields and construct cyclic algebras of arbitrary degree $n^2$ with Whitehead group that is arbitrarily large but finite, and also with infinite Whitehead group.
Bibliography: 15 titles.

Full text: PDF file (1186 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1976, 29:2, 167–176

Bibliographic databases:

UDC: 513.6
MSC: Primary 16A40, 16A18, 12A60, 12A65; Secondary 18F25
Received: 19.01.1976

Citation: V. P. Platonov, “The infinitude of the reduced Whitehead group in the Tannaka–Artin problem”, Mat. Sb. (N.S.), 100(142):2(6) (1976), 191–200; Math. USSR-Sb., 29:2 (1976), 167–176

Citation in format AMSBIB
\Bibitem{Pla76}
\by V.~P.~Platonov
\paper The infinitude of the reduced Whitehead group in the Tannaka--Artin problem
\jour Mat. Sb. (N.S.)
\yr 1976
\vol 100(142)
\issue 2(6)
\pages 191--200
\mathnet{http://mi.mathnet.ru/msb2869}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=412228}
\zmath{https://zbmath.org/?q=an:0352.16009}
\transl
\jour Math. USSR-Sb.
\yr 1976
\vol 29
\issue 2
\pages 167--176
\crossref{https://doi.org/10.1070/SM1976v029n02ABEH003660}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1976EZ91500003}


Linking options:
  • http://mi.mathnet.ru/eng/msb2869
  • http://mi.mathnet.ru/eng/msb/v142/i2/p191

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. I. Yanchevskii, “Reduced unitary $K$-theory and division rings over discretely valued Hensel fields”, Math. USSR-Izv., 13:1 (1979), 175–213  mathnet  crossref  mathscinet  zmath  isi
    2. V. I. Yanchevskii, “Reduced unitary $K$-theory. Aplications to algebraic groups”, Math. USSR-Sb., 38:4 (1981), 533–548  mathnet  crossref  mathscinet  zmath  isi
    3. A. E. Zalesskii, “Linear groups”, Russian Math. Surveys, 36:5 (1981), 63–128  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. Yu. L. Ershov, “Henselian valuations of division rings and the group $SK_1$”, Math. USSR-Sb., 45:1 (1983), 63–71  mathnet  crossref  mathscinet  zmath
    5. S. I. Adian, E. I. Zel'manov, G. A. Margulis, S. P. Novikov, A. S. Rapinchuk, L. D. Faddeev, V. I. Yanchevskii, “Vladimir Petrovich Platonov (on his 60th birthday)”, Russian Math. Surveys, 55:3 (2000), 601–610  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    6. Hazrat R. Wadsworth A.R., “Unitary Sk1 of Graded and Valued Division Algebras”, Proc. London Math. Soc., 103:Part 3 (2011), 508–534  crossref  mathscinet  zmath  isi
    7. Hazrat R. Wadsworth A.R., “Sk1 of Graded Division Algebras”, Isr. J. Math., 183:1 (2011), 117–163  crossref  mathscinet  zmath  isi
    8. A. R. Wadsworth, “Unitary SK1 of semiramified graded and valued division algebras”, manuscripta math, 139:3-4 (2012), 343  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:255
    Full text:49
    References:25
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019