Standard bases and some computations in rings of power series

DOI10.1016/S0747-7171(08)80039-9zbMath0709.13013MaRDI QIDQ921065

Thomas M. Becker

Publication date: 1990

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

zbMATH Keywords

formal power seriesBuchberger algorithmDixon's lemmaHironaka remainder

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Formal power series rings (13F25)

Related Items (10)

Numbers of generators of perfect ideals ⋮ When does a perturbation of the equations preserve the normal cone? ⋮ Algebraic approximation of Cohen-Macaulay algebras ⋮ Stability and Buchberger criterion for standard bases in power series rings ⋮ Formal groups, supersingular abelian varieties and tame ramification ⋮ Standard bases for local rings of branches and their modules of differentials ⋮ A generalization of Gröbner bases helps to compute singularity theory transformations ⋮ Extension of Hironaka's standard basis theorem for generalized power series ⋮ Reduction Mod p of Standard Bases ⋮ Hilbert function of local Artinian level rings in codimension two

Cites Work

• Unnamed Item
• Unnamed Item
• On the theory of graded structures
• Théorème de division et stabilité en géométrie analytique locale
• Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal. Translation from the German
• 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

This page was built for publication: Standard bases and some computations in rings of power series