Sampat Sharma

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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.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.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…

math.AC2026

Homotopy and Commutativity Principle

Ravi A. Rao, Sampat Sharma

In this article, we prove commutativity principal for linear, symplectic and transvection groups. This principle is a consequence of Quillen-Suslin local global principle and using…

Absence of torsion in orbit space

Generalised Mennicke-Newman lemma

Completion of skew completable unimodular rows

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

Homotopy and Commutativity Principle

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