Structure of \(\mathbb{A}^2\)-fibrations having fixed point free locally nilpotent derivations

DOI10.1016/j.jpaa.2021.106763zbMath1467.14155arXiv2001.07632OpenAlexW3164720031WikidataQ112882085 ScholiaQ112882085MaRDI QIDQ2040512

Janaki Raman Babu, Prosenjit Das

Publication date: 14 July 2021

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.07632

zbMATH Keywords

locally nilpotent derivationslicepolynomial algebraaffine fibrationresidual variablefixed point free

Mathematics Subject Classification ID

Derivations and commutative rings (13N15) Polynomials over commutative rings (13B25) Affine fibrations (14R25)

Related Items (2)

A criterion to determine residual coordinates of \(\mathbb{A}^{2}\)-fibrations ⋮ Rank and rigidity of locally nilpotent derivations of affine fibrations

Cites Work

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• A triviality criterion for \(\mathbb{A}^2\)-fibrations over a ring containing \(\mathbb{Q}\)
• On cancellation of variables of the form \(b T^n - a\) over affine normal domains
• Structure of \(\mathbb A^2\)-fibrations over one-dimensional Noetherian domains
• Polynomial ring in two variables over a D.V.R.: A criterion
• On free holomorphic \({\mathbb{C}}\)-actions on \({\mathbb{C}}^ n\) and homogeneous Stein manifolds
• Polynomial fibre rings of algebras over noetherian rings
• On Zariski problem
• Affine surfaces containing cylinderlike open sets
• On the absence of nontrivial separable forms of the affine plane
• On the \(R\)-invariance of \(R[X\)]
• Locally polynomial algebras are symmetric algebras
• Locally nilpotent derivations over a UFD and an application to rank two locally nilpotent derivations of \(k[X_1,\dots,X_n\)]
• Fixed point free locally nilpotent derivations of \(\mathbb A^2\)-fibrations
• A note on residual variables of an affine fibration
• The cancellation problem over Noetherian one-dimensional domains
• Modules projectifs universels
• Derivations of \(R[X,Y,Z\) with a slice]
• A class of counterexamples to the Cancellation Problem for arbitrary rings
• Families of Affine Fibrations
• Kernel of locally nilpotent 𝑅-derivations of 𝑅[𝑋,𝑌]
• Nonuniqueness of Coefficient Rings in a Polynomial Ring
• Projective algebras
• On the Jacobian conjecture
• On seminormality
• Algebraic theory of locally nilpotent derivations
• Derivations having divergence zero on \(R[X,Y\).]

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