On Roberts' counterexample to the fourteenth problem of Hilbert

DOI10.1016/S0022-4049(97)00059-5zbMath0887.13009OpenAlexW2021897325WikidataQ125027710 ScholiaQ125027710MaRDI QIDQ1376308

Masayoshi Miyanishi, Hideo Kojima

Publication date: 6 May 1998

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(97)00059-5

zbMATH Keywords

polynomial algebrainvariant subringnilpotent derivationadditive group schemenot finitely generated algebra

Mathematics Subject Classification ID

Group actions on varieties or schemes (quotients) (14L30) Actions of groups on commutative rings; invariant theory (13A50) Commutative rings and modules of finite generation or presentation; number of generators (13E15)

Related Items (14)

A condition for finite generation of the kernel of a derivation. ⋮ Linear counterexamples to the fourteenth problem of Hilbert ⋮ A counterexample to the fourteenth problem of Hilbert in dimension four ⋮ A simple proof of Nowicki's conjecture on the kernel of an elementary derivation ⋮ Hilbert's fourteenth problem and algebraic extensions ⋮ Hilbert's fourteenth problem and field modifications ⋮ Van den Essen's conjecture on the kernel of a derivation having a slice ⋮ A counterexample to Hilbert's fourteenth problem in dimension 5 ⋮ A counterexample to Hilbert's fourteenth problem in dimension six ⋮ 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

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• An infinitely generated symbolic blow-up in a power series ring and a new counterexample to Hilbert's fourteenth problem
• Lectures on curves on rational and unirational surfaces
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Séconde partie)

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