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Fundam. Prikl. Mat., 1995, Volume 1, Issue 2, Pages 545–548 (Mi fpm71)  

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

Short communications

On the structure of the symplectic group over polynomial rings with regular coefficients

V. I. Kopeiko

Kalmyckia State University

Abstract: In this note we prove the following result. Let $A$ be a ring of the geometric type or $A=C[[T_1,\ldots,T_{m}]]$, where $C$ is a regular ring and $\dim C\leq1$. Then the group $\operatorname{Sp}_{2r}(A[X_1,\ldots,X_{n}])$ ($r\geq2$) is generated by elementary symplectic matrices.

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Received: 01.01.1995

Citation: V. I. Kopeiko, “On the structure of the symplectic group over polynomial rings with regular coefficients”, Fundam. Prikl. Mat., 1:2 (1995), 545–548

Citation in format AMSBIB
\Bibitem{Kop95}
\by V.~I.~Kopeiko
\paper On the structure of the symplectic group over polynomial rings with regular coefficients
\jour Fundam. Prikl. Mat.
\yr 1995
\vol 1
\issue 2
\pages 545--548
\mathnet{http://mi.mathnet.ru/fpm71}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1790985}
\zmath{https://zbmath.org/?q=an:0867.20040}


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    Erratum

    This publication is cited in the following articles:
    1. 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
    2. Stavrova A., “Homotopy Invariance of Non-Stable K-1-Functors”, J. K-Theory, 13:2 (2014), 199–248  crossref  mathscinet  isi  elib
  • Фундаментальная и прикладная математика
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