On the rigidity of small domains

DOI10.1016/j.jalgebra.2004.09.015zbMath1094.13042arXivmath/0406412OpenAlexW2069673647MaRDI QIDQ1764826

Anthony J. Crachiola, Leonid G. Makar-Limanov

Publication date: 22 February 2005

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0406412

zbMATH Keywords

locally nilpotent derivationlocally finite iterative higher derivationAK invariant

Mathematics Subject Classification ID

Actions of groups on commutative rings; invariant theory (13A50) Derivations and commutative rings (13N15) Polynomials over commutative rings (13B25) Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) (14R10)

Related Items

A note on the cancellation property of k[X, Y] ⋮ Cancellation for Surfaces Revisited ⋮ Laurent Cancellation for Rings of Transcendence Degree One Over a Field ⋮ ML invariant of the symmetric algebra of a projective module over a one dimensional affine domain ⋮ Additive group actions on affine \(\mathbb{T}\)-varieties of complexity one in arbitrary characteristic ⋮ The automorphism group of a rigid affine variety ⋮ An affine version of a theorem of Nagata ⋮ Actions of the additive group \(G_a\) on certain noncommutative deformations of the plane ⋮ An algebraic proof of a cancellation theorem for surfaces ⋮ Noncommutative analogues of a cancellation theorem of Abhyankar, Eakin, and Heinzer ⋮ On automorphisms of Danielewski surfaces ⋮ The hypersurface 𝑥+𝑥²𝑦+𝑧²+𝑡³=0 over a field of arbitrary characteristic ⋮ Notes on the Kernels of Locally Finite Higher Derivations in Polynomial Rings ⋮ Cancellation of Morita and skew types ⋮ Zariski cancellation problem for non-domain noncommutative algebras ⋮ Canonical factorization of the quotient morphism for an affine \(\mathbb{G}_{a}\)-variety ⋮ An algebraic characterization of the affine three space ⋮ Horizontal Ga-actions on affine T-varieties of complexity one

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On affine-ruled rational surfaces
• On Zariski problem
• Affine surfaces containing cylinderlike open sets
• On complex affine surfaces with \(\mathbb{C}^ +\)-action
• Affine surfaces with \(AK(S)=\mathbb C\).
• Polynomial automorphisms and the Jacobian conjecture
• On the uniqueness of the coefficient ring in a polynomial ring
• On the cancellation problem for surfaces
• Nonuniqueness of Coefficient Rings in a Polynomial Ring
• On the group of automorphisms of a surface \(x^ny= P(z)\)