On some properties of elementary derivations in dimension six

DOI10.1016/S0022-4049(99)00121-8zbMath1014.13008OpenAlexW2126654728MaRDI QIDQ5929286

Joseph Khoury

Publication date: 3 November 2002

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

Full work available at URL: https://doi.org/10.1016/s0022-4049(99)00121-8

zbMATH Keywords

Hilbert's fourteenth problemlocally nilpotent derivationsUFD

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Actions of groups on commutative rings; invariant theory (13A50) Derivations and commutative rings (13N15) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15)

Related Items (8)

A condition for finite generation of the kernel of a derivation. ⋮ A simple proof of Nowicki's conjecture on the kernel of an elementary derivation ⋮ Van den Essen's conjecture on the kernel of a derivation having a slice ⋮ A generalization of Roberts' counterexample to the fourteenth problem of Hilbert ⋮ A counterexample to the fourteenth problem of Hilbert in dimension three ⋮ A Gröbner basis approach to solve a conjecture of Nowicki ⋮ A linear counterexample to the Fourteenth Problem of Hilbert in dimension eleven ⋮ Fields defined by locally nilpotent derivations and monomials

Cites Work

• Unnamed Item
• An infinitely generated symbolic blow-up in a power series ring and a new counterexample to Hilbert's fourteenth problem
• Rings of constants for \(k\)-derivations in \(k[x_ 1,\dots ,x_ n\)]
• The kernel of a derivation
• 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
• Triangular monomial derivations on \(k[X_1,X_2,X_3,X_4\) have kernel generated by at most four elements]
• A counterexample to Hilbert's fourteenth problem in dimension 5
• A counterexample to Hilbert's fourteenth problem in dimension six
• Fields of G_a Invariants are Ruled
• G_a actions on c₃ and c₇

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