RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zap. Nauchn. Sem. POMI:
Year:
Volume:
Issue:
Page:
Find






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


Zap. Nauchn. Sem. POMI, 2011, Volume 388, Pages 270–308 (Mi znsl4114)  

Homogeneous skew-fields of non-commutative rational functions and their reduced Whitehead groups

V. I. Yanchevskiĭ

Institute of Mathematics of the National Academy of Sciences of Belarus

Abstract: A construction of skew-fields of non-commutative rational functions is studied. We discuss and prove criterions for such skew-fields to be homogeneous and finite-dimensional over their centers and describe relations between some objects defined in terms of the skew-fields of constants, which help to compute reduced Whitehead groups of corresponding skew-fields of non-commutative rational functions. In particular we present a proof of one previous result of V. P. Platonov and the author about reduced Whitehead groups of skew-fields of non-commutative rational functions announced in 1979 and obtain in non-Henselian case of such skew-fields analogues of all results of Yu. L. Ershov for Henselian situation.

Key words and phrases: reduced Whitehead group, skew-field of non-commutative rational functions, special linear group of finite-dimensional central simple algebra, skew polynomial ring.

Full text: PDF file (750 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences (New York), 2012, 183:5, 727–747

UDC: 514.142
Received: 02.04.2011

Citation: V. I. Yanchevskiǐ, “Homogeneous skew-fields of non-commutative rational functions and their reduced Whitehead groups”, Problems in the theory of representations of algebras and groups. Part 21, Zap. Nauchn. Sem. POMI, 388, POMI, St. Petersburg, 2011, 270–308; J. Math. Sci. (N. Y.), 183:5 (2012), 727–747

Citation in format AMSBIB
\Bibitem{Yan11}
\by V.~I.~Yanchevski{\v\i}
\paper Homogeneous skew-fields of non-commutative rational functions and their reduced Whitehead groups
\inbook Problems in the theory of representations of algebras and groups. Part~21
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 388
\pages 270--308
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4114}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2012
\vol 183
\issue 5
\pages 727--747
\crossref{https://doi.org/10.1007/s10958-012-0836-x}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84862295875}


Linking options:
  • http://mi.mathnet.ru/eng/znsl4114
  • http://mi.mathnet.ru/eng/znsl/v388/p270

    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
  • Записки научных семинаров ПОМИ
    Number of views:
    This page:162
    Full text:51
    References:24

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