局部环上特殊线性群的u-伸缩换位子生成

The special linear groups over local rings generated by commutators dilatations

设R是局部环，J是R的根，U（R）是R中单位元素集合。在一般线性群GLn（R）（n≥2）中与u■In-1相似的元素称为一个U－伸缩，其中u∈U（R）。在|R／J|＞2的假设下，证明SLn（R）可由u－伸缩构成的换位子生成。并在R是域时，在|R|＝3或4的假设下，确定SL2（R）中u－伸缩换位子生成个数。

Let R be a local ring and J denote the radical of R, the author shows that every element of SLn(R) represent as a product of corrunutators dilatations with |R/J|>2, and the shortest length l(SL2(F)) generated by commutators dilatations detendned where F is a field with |F|=3 or 4.