FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1995, VOLUME 1, NUMBER 4, PAGES 1111-1114

On the structure of the special linear groups over Laurent polynomial rings

V.I.Kopeiko

In this note we prove the following result. Let C be a regular ring such that SK1(C) = 0. Then the groups $SL_r (C [[T_1,\ldots,T_m]] [X_1^{\pm 1},\ldots,X_n^{\pm 1},Y_1,\ldots,Y_s])$ are generated by elementary matrices for all integers $r \geq \max(3,\dim C+2)$.

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