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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Fundam. Prikl. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Fundam. Prikl. Mat., 1995, Volume 1, Issue 3, Pages 661–668 (Mi fpm94)  

This article is cited in 2 scientific papers (total in 2 papers)

On the general linear group over weak Noetherian associative algebras

I. Z. Golubchik

Bashkir State Pedagogical University

Abstract: Let $R$ be a weak Noetherian algebra with unity element over an infinite field, $I$ an ideal in $R$, $n\geq3$, $E_n(R)$ the elementary subgroup in the general linear group $GL_n(R)$, $E_n(R,I)$ the normal subgroup in $E_n(R)$ generated by the elementary matrices $1+\lambda e_{ij}$, $\lambda\in I$, $1\leq i\neq j\leq n$, $GL_n(R,I)$ the kernel and $C_n(R,I)$ the preimage of the center of the homomorphism $GL_n(R)\to GL_n(R/I)$ respectively. It is proved that if $G$ is a subgroup of $GL_n(R)$, then it is normalized by $E_n(R)$ if and only if $E_n(R,F)\subseteq G\subseteq C_n(R,F)$ for some ideal $F$ of $R$; $[C_n(R,F),E_n(R)]=E_n(R,F)$ and in particular the groups $E_n(R)$ and $E_n(R,F)$ are normal in $GL_n(R)$ for all ideals $F$ of $R$.

Full text: PDF file (309 kB)
References: PDF file   HTML file

Bibliographic databases:
UDC: 512.544.6
Received: 01.04.1995

Citation: I. Z. Golubchik, “On the general linear group over weak Noetherian associative algebras”, Fundam. Prikl. Mat., 1:3 (1995), 661–668

Citation in format AMSBIB
\Bibitem{Gol95}
\by I.~Z.~Golubchik
\paper On the general linear group over weak Noetherian associative algebras
\jour Fundam. Prikl. Mat.
\yr 1995
\vol 1
\issue 3
\pages 661--668
\mathnet{http://mi.mathnet.ru/fpm94}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1788549}
\zmath{https://zbmath.org/?q=an:0867.20037}


Linking options:
  • http://mi.mathnet.ru/eng/fpm94
  • http://mi.mathnet.ru/eng/fpm/v1/i3/p661

    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. Stepanov, A, “Decomposition of transvections: A theme with variations”, K-Theory, 19:2 (2000), 109  crossref  mathscinet  zmath  isi
    2. N. A. Vavilov, A. V. Stepanov, “Linear groups over general rings. I. Generalities”, J. Math. Sci. (N. Y.), 188:5 (2013), 490–550  mathnet  crossref  mathscinet
  • Фундаментальная и прикладная математика
    Number of views:
    This page:187
    Full text:70
    References:33
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020