Advertisement

Israel Journal of Mathematics

, Volume 225, Issue 1, pp 403–410 | Cite as

On bounded elementary generation for SL n over polynomial rings

  • Bogdan Nica
Article
  • 45 Downloads

Abstract

Let F[X] be the polynomial ring over a finite field F. It is shown that, for n ≥ 3, the special linear group SL n (F[X]) is boundedly generated by the elementary matrices.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M. Abért, A. Lubotzky and L. Pyber, Bounded generation and linear groups, International Journal of Algebra and Computation 13 (2003), 401–413.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    S. I. Adian and J. Mennicke, On bounded generation of SLn(Z), International Journal of Algebra and Computation 2 (1992), 357–365.MathSciNetCrossRefGoogle Scholar
  3. [3]
    L. Bary-Soroker, Dirichlet’s theorem for polynomial rings, Proceedings of the American Mathematical Society 137 (2009), 73–83.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    H. Bass, K-theory and stable algebra, Publications Mathématiques. Institut de Hautes Études Scientifiques 22 (1964), 5–60.CrossRefGoogle Scholar
  5. [5]
    D. Carter and G. Keller, Bounded elementary generation of SLn(O), American Journal of Mathematics 105 (1983), 673–687.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    D. Carter and G. Keller, Elementary expressions for unimodular matrices, Communications in Algebra 12 (1984), 379–389.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    D. R. Heath-Brown, Zero-free regions for Dirichlet L-functions, and the least prime in an arithmetic progression, Proceedings of the London Mathematical Society 64 (1992), 265–338.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    B. Nica, A true relative of Suslin’s normality theorem, L’Enseignement Mathématique 61 (2015), 151–159.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    M. Rosen, Number Theory in Function Fields, Graduate Texts in Mathematics, Vol. 210, Springer-Verlag, New York, 2002.Google Scholar
  10. [10]
    A. Stepanov, Structure of Chevalley groups over rings via universal localization, Journal of Algebra 450 (2016), 522–548.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    W. van der Kallen, SL3(C[X]) does not have bounded word length, in Algebraic Ktheory, Part I (Oberwolfach, 1980), Lecture Notes in Mathematics, Vol. 966, Springer, Berlin–New York, 1982, pp. 357–361.Google Scholar
  12. [12]
    D. Witte Morris, Bounded generation of SL(n,A) (after D. Carter, G. Keller, and E. Paige), New York Journal of Mathematics 13 (2007), 383–421.MathSciNetzbMATHGoogle Scholar

Copyright information

© Hebrew University of Jerusalem 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada

Personalised recommendations