On the structure of the special linear groups over Laurent polynomial rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 1111-1114
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In this note we prove the following result. Let $C$ be a regular ring such that $\mathrm{SK}(C)=0$. Then the groups $SL_r\bigl(C\bigl[[T_1,\ldots,T_m]\bigr]
\left[X_1^{\pm1},\ldots,X_n^{\pm 1},Y_1,\ldots,Y_s\right]\bigr)$ are generated by elementary matrices for all integers $r\geq\max(3,\dim C+2)$.
@article{FPM_1995_1_4_a21,
author = {V. I. Kopeiko},
title = {On the structure of the special linear groups over {Laurent} polynomial rings},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {1111--1114},
publisher = {mathdoc},
volume = {1},
number = {4},
year = {1995},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a21/}
}
TY - JOUR AU - V. I. Kopeiko TI - On the structure of the special linear groups over Laurent polynomial rings JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 1995 SP - 1111 EP - 1114 VL - 1 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a21/ LA - ru ID - FPM_1995_1_4_a21 ER -
V. I. Kopeiko. On the structure of the special linear groups over Laurent polynomial rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 1111-1114. http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a21/