Sampat Sharma

activity

20172022

most citedNice group structure on the elementary orbit space of unimodular rows

3 citations · 4 across the 8 of their papers we have counts for

collaborators

Showing 2020Show all

4 papers · 1 filter

math.AC2020

Absence of torsion in orbit space

Sampat Sharma

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 $\frac{U m _{d + 1} ( R [ X ])}{E _{d + 1} ( R [ X ])}$ has no $k$ -torsion, pr…

math.AC2020

On completion of unimodular rows over polynomial extension of finitely generated rings over $Z$

Sampat Sharma

In this article, we prove that if $R$ is a finitely generated ring over $Z$ of dimension $d, d \geq 2, \frac{1}{d !} \in R$ , then any unimodular row over $R [X]$ of length $d+1…

math.AC2020★ 1 cited

The quotient Unimodular Vector group is nilpotent

Reema Khanna, Selby Jose, Sampat Sharma +1

Jose-Rao introduced and studied the Special Unimodular Vector group $S U m_{r} (R)$ and $E U m_{r} (R)$ , its Elementary Unimodular Vector subgroup. They proved that for $r \geq 2$ , $EUm_r(R)…

math.AC2020

On the first row map $G L_{d + 1} (R) ⟶ \frac{U m _{d + 1} ( R )}{E _{d + 1} ( R )}$

Sampat Sharma

In this paper, we prove that there is group homomorphism from general linear group over a polynomial extension of a local ring to the W. van der Kallen group.

Absence of torsion in orbit space

On completion of unimodular rows over polynomial extension of finitely generated rings over Z

The quotient Unimodular Vector group is nilpotent

On the first row map GLd+1​(R)⟶Ed+1​(R)Umd+1​(R)​

On completion of unimodular rows over polynomial extension of finitely generated rings over $Z$

On the first row map $G L_{d + 1} (R) ⟶ \frac{U m _{d + 1} ( R )}{E _{d + 1} ( R )}$