Pankaj Shukla

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math.AC2025

A Class of simple derivations of polynomial ring $k [x_{1}, x_{2}, \dots, x_{n}]$

Sumit Chandra Mishra, Dibyendu Mondal, Pankaj Shukla

Let $k$ be a field of characteristic zero. Let $m$ and $I^\pm$ be positive integers. For $n \geq 2$ , let $R_{n} = k [x_{1}, x_{2}, \dots, x_{n}]$ with the $k$ -derivation $d_{n}$ given by $d_n=(1-x_1x_…

math.AC2025

On the Isotropy Groups of Non-Invertible Simple Derivations

Sumit Chandra Mishra, Dibyendu Mondal, Pankaj Shukla

Let $k$ be a field of characteristic zero, and let $i$ and $n$ be positive integers with $i \geq 2$ and $n > i$ . Consider a non-invertible $k$ -derivation $d_{i}$ of the polynomial ring…

math.AC2024

Simple derivations in two variables

Anand Parkash, Pankaj Shukla

Let $k$ be a field of characteristic zero. If $c_{1}, c_{2} \in k ∖ {0}, s, t \geq 1$ and $u \geq 0$ , then it is shown that the $k$ -derivations $\partial_x + x^u(c_1x^ty^s+c_2)…

A Class of simple derivations of polynomial ring k[x1​,x2​,…,xn​]

On the Isotropy Groups of Non-Invertible Simple Derivations

Simple derivations in two variables

A Class of simple derivations of polynomial ring $k [x_{1}, x_{2}, \dots, x_{n}]$