论文标题
在轨道空间中没有扭转
Absence of torsion in orbit space
论文作者
论文摘要
在本文中，我们证明，如果$ r $是尺寸$ d的本地环，$ $ d \ geq 2 $和$ \ frac {1} {d！} \ in r $ in r $，则组$ \ frac {um_ {d+1}（d+1}（r [x]}（r [x]）}} gl_ {1}（r）。$我们还证明，如果$ r $是常规的尺寸环$ d，$ $ $ d \ geq 2 $和$ \ frac {1} {d！} \在r $中，则$ e_ {d+1}（d+1}（r）$在$ e_ {d+1}（r）上，$ _ {d+1} $ and $ and $ and $ and $ can d+and $ r）在$ um_ {d+1}（r [x]）上进行过渡。$
In this paper, we prove that if $R$ is a local ring of dimension $d,$ $d\geq 2$ and $\frac{1}{d!}\in R$ then the group $\frac{Um_{d+1}(R[X])}{E_{d+1}(R[X])}$ has no $k$-torsion, provided $k\in GL_{1}(R).$ We also prove that if $R$ is a regular ring of dimension $d,$ $d\geq 2$ and $\frac{1}{d!}\in R$ such that $E_{d+1}(R)$ acts transitively on $Um_{d+1}(R)$ then $E_{d+1}(R[X])$ acts transitively on $Um_{d+1}(R[X]).$
