Sampat Sharma

collaborators

7 papers

math.AC2026

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.RA2026

Unimodular rows over affine algebras over algebraic closure of a finite field

Sampat Sharma

In this article, we prove that if $R$ is an affine algebra of dimension $d \geq 4$ over $F_{p}$ and $1/ (d - 1)! \in R,$ then any unimodular row over $R$ of length…

math.AC2026

Generalised Mennicke-Newman lemma

Sampat Sharma

Mennicke--Newman lemma for unimodular rows was used by W. van der Kallen to give a group structure on the orbit set $\frac{U m _{n} ( R )}{E _{n} ( R )}$ for a commutative noetherian ring o…

math.KT2026

Applications of Swan's Bertini to unimodular rows

Manoj K. Keshari, Sampat Sharma

Let $R$ be an affine algebra of dimension $d \geq 4$ over a perfect field $k$ of char $\neq = 2$ and $I$ be an ideal of $R$ . Then - Um $_{d + 1} (R, I) / E_{d + 1} (R, I)$ has nice group s…

math.AC2026

Completion of skew completable unimodular rows

Sampat Sharma

Skew completable unimodular rows of odd length are completable over polynomial extension of a local ring if dimension of local ring and length of unimodular rows are same.

math.AC2026

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…

Absence of torsion in orbit space

Unimodular rows over affine algebras over algebraic closure of a finite field

Generalised Mennicke-Newman lemma

Applications of Swan's Bertini to unimodular rows

Completion of skew completable unimodular rows

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

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