Triangular derivations of \({\mathbf k}[X_1,X_2,X_3,X_4]\)

DOI10.1006/jabr.2001.8763zbMath1018.13013OpenAlexW2019330660MaRDI QIDQ5946420

Daniel Daigle, Gene Freudenburg

Publication date: 27 February 2002

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

Full work available at URL: https://doi.org/10.1006/jabr.2001.8763

zbMATH Keywords

triangular derivation

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Derivations and commutative rings (13N15)

Related Items (12)

A condition for finite generation of the kernel of a derivation. ⋮ A counterexample to the fourteenth problem of Hilbert in dimension four ⋮ Additive group actions with finitely generated invariants ⋮ Proper \(G_a\)-actions on \(\mathbb C^4\) preserving a coordinate ⋮ Triangular 𝐺ₐ actions on 𝐂⁴ ⋮ On finite generation of kernels of locally nilpotent \(R\)-derivations of \(R[X,Y,Z\)] ⋮ The epimorphism theorem and its generalizations ⋮ The Zariski cancellation problem and related problems in affine algebraic geometry ⋮ Structure of the kernel of a locally nilpotent derivation on an affine normal domain ⋮ A note on a class of rings found as \(G_a\)-invariants for locally trivial actions on normal affine varieties ⋮ A counterexample to the fourteenth problem of Hilbert in dimension three ⋮ Fields defined by locally nilpotent derivations and monomials

Cites Work

• Krull dimension, transcendence degree and subalgebras of finitely generated algebras
• Locally nilpotent derivations over a UFD and an application to rank two locally nilpotent derivations of \(k[X_1,\dots,X_n\)]
• An algorithm to compute the invariant ring of a \(G_ a\)-action on an affine variety
• A counterexample to Hilbert's fourteenth problem in dimension 5
• Fields of G_a Invariants are Ruled
• A note on triangular derivations of $\mathbf {k}[X_1,X_2,X_3,X_4$]
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