On separable A 2and A 3-forms AMARTYA KUMAR DUTTA, NEENA GUPTA, ANIMESH LAHIRI Nagoya Mathematical Journal, 2020 In this paper, we will prove that any $\\mathbb{A}^{3}$-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 Kambayashi on the triviality of separable $\\mathbb{A}^{2}$-forms over a field $k$ extends to $\\mathbb{A}^{2}$-forms over any one-dimensional Noetherian domain containing $\\mathbb{Q}$.
A note on partial coordinate system in a polynomial ring Animesh Lahiri Communications in Algebra, 2019 Berson et al. proved that for a non-zero divisor a in a commutative ring R containing if the polynomials in form a partial coordinate system over the rings Ra and then form a partial coordinate system over the ring R. In this note, we show that the theory of residual variables of Bhatwadekar and Dutta and its recent extension by Das and Dutta, extends their result to the case when a is an arbitrary element of A.
