Stability and Buchberger criterion for standard bases in power series rings

DOI10.1016/0022-4049(90)90028-GzbMath0707.13008OpenAlexW2010539187MaRDI QIDQ919417

Thomas M. Becker

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1016/0022-4049(90)90028-g

zbMATH Keywords

Gröbner basespower series ringcomputabilitystandard basesBuchsberger algorithm

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Formal power series rings (13F25)

Related Items (10)

Finite determinacy and approximation of flat maps ⋮ Standard bases in mixed power series and polynomial rings over rings ⋮ Equisingular algebraic approximation of real and complex analytic germs ⋮ Algebraic approximation of Cohen-Macaulay algebras ⋮ A generalization of Gröbner bases helps to compute singularity theory transformations ⋮ Lefschetz extensions, tight closure and big Cohen-Macaulay algebras ⋮ Standard bases in \(Kt_1,\ldots ,t_m[x_1,\ldots ,x_n^s\)] ⋮ Topological rewriting systems applied to standard bases and syntactic algebras ⋮ Reduction Mod p of Standard Bases ⋮ Embedding codimension of the space of arcs

Cites Work

• Unnamed Item
• Standard bases and some computations in rings of power series
• Stability of Gröbner bases
• The Gröbner fan of an ideal
• Comments on the translation of my PhD thesis: ``An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal
• Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• Admissible orders and linear forms

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