Geodesic
On the structure of the symplectic group over polynomial rings with regular coefficients
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 2, pp. 545-548 
V. I. Kopeiko. On the structure of the symplectic group over polynomial rings with regular coefficients. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 2, pp. 545-548. http://geodesic.mathdoc.fr/item/FPM_1995_1_2_a16/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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

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