Geodesic
The stabilization of symplectic groups over a~polynomial ring
Sbornik. Mathematics, Tome 34 (1978) no. 5, pp. 655-669

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We prove that if $B$ is a polynomial ring over a field, then for $r\geqslant2$, any element of $Sp_{2r}B$ can be written as a product of elementary symplectic matrices over $B$. We also prove a stabilization theorem for the symplectic $K_1$-functor in the case of polynomial rings and Laurent rings. Bibliography: 6 titles. 
@article{SM_1978_34_5_a5,
     author = {V. I. Kopeiko},
     title = {The stabilization of symplectic groups over a~polynomial ring},
     journal = {Sbornik. Mathematics},
     pages = {655--669},
     publisher = {mathdoc},
     volume = {34},
     number = {5},
     year = {1978},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1978_34_5_a5/}
}
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V. I. Kopeiko. The stabilization of symplectic groups over a~polynomial ring. Sbornik. Mathematics, Tome 34 (1978) no. 5, pp. 655-669. http://geodesic.mathdoc.fr/item/SM_1978_34_5_a5/