Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Absence of torsion in orbit space   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 $Um_{d+1}(R[X]).$

25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph