A Gröbner basis approach to solve a conjecture of Nowicki

DOI10.1016/j.jsc.2008.05.004zbMath1160.13022OpenAlexW2008607833WikidataQ123230417 ScholiaQ123230417MaRDI QIDQ999091

Joseph Khoury

Publication date: 30 January 2009

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2008.05.004

zbMATH Keywords

elimination theorylocally nilpotent derivations

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Derivations and commutative rings (13N15) Group actions on affine varieties (14R20)

Related Items (9)

A simple proof of Nowicki's conjecture on the kernel of an elementary derivation ⋮ On Nowicki's conjecture: a survey and a new result ⋮ Weitzenböck derivations of free metabelian Lie algebras ⋮ Separating invariants for arbitrary linear actions of the additive group ⋮ The Nowicki conjecture for free metabelian Lie algebras ⋮ Another proof of the Nowicki conjecture ⋮ Generalized Nowicki conjecture ⋮ The Nowicki conjecture for relatively free algebras ⋮ On simple modules of the \(n\)-th Schrödinger algebra

Cites Work

• On the hypersurface \(x+x^2y+z^2+t^3=0\) in \(\mathbb{C}^4\) or a \(\mathbb{C}^3\)-like threefold which is not \(\mathbb{C}^3\)
• On Roberts' counterexample to the fourteenth problem of Hilbert
• Über die Invarianten von linearen Gruppen
• A counterexample to Hilbert's fourteenth problem in dimension 5
• A counterexample to Hilbert's fourteenth problem in dimension six
• On some properties of elementary derivations in dimension six
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