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.

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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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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/

[1] Kopeiko V. I., “Stabilizatsiya simplekticheskoi gruppy nad koltsami mnogochlenov”, Mat. sbornik, 106:1 (1978), 94–107 | MR | Zbl

[2] Kopeiko V. I., “O strukture simplekticheskoi gruppy kolets mnogochlenov nad regulyarnymi koltsami razmernosti $\le 1$”, UMN, 47:4 (1992), 193–194 | MR | Zbl

[3] Grunewald F., Mennicke J., Vaserstein L., “On symplectic groups over polynomial rings”, Math. Z., 206 (1991), 35–56 | DOI | MR | Zbl

[4] Lam T.-Y., “Serre's conjecture”, Lect. Notes Math., 635, 1978, 3–210

[5] Vorst T., “The general linear groups of polynomial rings over regular rings”, Commun. Algebra, 9:5 (1981), 499–509 | DOI | MR | Zbl

[6] Suslin A. A., “O strukture spetsialnoi lineinoi gruppy nad koltsami mnogochlenov”, Izv. AN SSSR. Ser. matem., 41:2 (1977), 235–252 | MR | Zbl