arXiv subjects
Publications and source records attributed to Animesh Lahiri.
In this paper, for a field $k$ of characteristic zero and a finitely generated $k$-algebra $R$, we give a set of generators for the image ideals of irreducible nice and quasi-nice $R$-derivations on the polynomial ring $R[X,Y]$, where $R$ is a UFD.
In this paper, we give a characterization of locally nilpotent derivations on $\mathbb{A}^2$-fibrations over Noetherian domains containing $\mathbb{Q}$ having kernel isomorphic to an $\mathbb{A}^1$-fibration.
In this paper, we study the isotropy subgroups of some almost rigid domains and give necessary and sufficient conditions for an automorphism to be in the isotropy subgroup.
J. Berson, J. W. Bikker and A. van den Essen proved that for a non-zerodivisor $a$ in a commutative ring $R$ containing $Q$ if the polynomials $f_1,\dots,f_{n-1}$ in $R[X_1,\dots,X_n]$ form a partial coordinate system over the rings $R_a$ and $\dfrac{R}{aR}$ then $f_1,\dots,f_{n-1}$ form a partial coordinate system over the ring $R$. In this note we show that the theory of residual variables of Bhatwadekar-Dutta and its recent extension by Das-Dutta, extends their result to the case when $a$ is an arbitrary element of $A$.
In a recent paper, M. E. Kahoui and M. Ouali have proved that over an algebraically closed field $k$ of characteristic zero, residual coordinates in $k[X][Z_1,\dots,Z_n]$ are one-stable coordinates. In this paper we extend their result to the case of an algebraically closed field $k$ of arbitrary characteristic. In fact, we show that the result holds when $k[X]$ is replaced by any one-dimensional seminormal domain $R$ which is affine over an algebraically closed field $k$. For our proof, we extend a result of S. Maubach giving a criterion for a polynomial of the form $a(X)W+P(X,Z_1,\dots,Z_n)$ to be a coordinate in $k[X][Z_1,\dots,Z_n,W]$. Kahoui and Ouali had also shown that over a Noetherian $d$-dimensional ring $R$ containing $Q$ any residual coordinate in $R[Z_1,\dots,Z_n]$ is an $r$-stable coordinate, where $r=(2^d-1)n$. We will give a sharper bound for $r$ when $R$ is affine over an algebraically closed field of characteristic zero.
In this paper, we will prove that any $\A^3$-form over a field $k$ of characteristic zero is trivial provided it has a locally nilpotent derivation satisfying certain properties. We will also show that the result of T. Kambayashi on the triviality of separable $\A^2$-forms over a field $k$ extends to $\A^2$-forms over any one-dimensional Noetherian domain containing $\bQ$.