The infiniteness of the SAGBI bases for certain invariant rings.

zbMath1045.13012MaRDI QIDQ1847611

Shigeru Kuroda

Publication date: 10 December 2002

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

finite permutation groupspolynomial invariantsLaurent polynomialfinite generation of initial algebrasinitial termsmultiplicative ordersSAGBIsubalgebra analogue to Gröbner bases for idealssubalgebra of invariants of a permutation group

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Actions of groups on commutative rings; invariant theory (13A50) Commutative rings and modules of finite generation or presentation; number of generators (13E15) Group actions on affine varieties (14R20)

Related Items (12)

Weighted multidegrees of polynomial automorphisms over a domain ⋮ A new class of finitely generated polynomial subalgebras without finite SAGBI bases ⋮ Completion of real fans and Zariski-Riemann spaces ⋮ Invariant \(\mathrm G^2\mathrm V\) algorithm for computing SAGBI-Gröbner bases ⋮ MFO-RIMS tandem workshop: Symmetries on polynomial ideals and varieties. Abstracts from the MFO-RIMS tandem workshop held September 5--11, 2021 (hybrid meeting) ⋮ Separability of wild automorphisms of a polynomial ring ⋮ Two Points of the Boundary of Toric Geometry ⋮ A topological structure on certain initial algebras. ⋮ On initial algebras of multiplicative invariants ⋮ A generalization of Roberts' counterexample to the fourteenth problem of Hilbert ⋮ SAGBI bases for rings of invariant Laurent polynomials ⋮ Toric geometry and the Semple-Nash modification

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