Dynamical Gröbner bases over Dedekind rings

DOI10.1016/j.jalgebra.2010.04.014zbMath1200.13047OpenAlexW2018462023MaRDI QIDQ984989

Amina Hadj Kacem, Ihsen Yengui

Publication date: 20 July 2010

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2010.04.014

zbMATH Keywords

Gröbner basisconstructive mathematicsGröbner ringsDedekind ringsdynamical Gröbner basisideal membership problemprincipal rings

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) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (20)

The Gröbner ring conjecture in the lexicographic order case ⋮ Standard bases in mixed power series and polynomial rings over rings ⋮ The trailing terms ideal over a valuation domain ⋮ Noether normalization theorem and dynamical Gröbner bases over Bézout domains of Krull dimension 1 ⋮ A negative answer to a question about leading terms ideals of polynomial ideals ⋮ The Gröbner ring conjecture in one variable ⋮ On the leading terms ideals of polynomial ideals over a valuation ring ⋮ An extension of Gröbner basis theory to indexed polynomials without eliminations ⋮ Semi-ring Based Gröbner–Shirshov Bases over a Noetherian Valuation Ring ⋮ Corrigendum to ``Dynamical Gröbner bases and to ``Dynamical Gröbner bases over Dedekind rings ⋮ Computing the \textbf{V}-saturation of finitely-generated submodules of \(\mathbf{V} [X^m\) where \textbf{V} is a valuation domain] ⋮ Computing syzygies over \(V [X_1, \ldots, X_k\), \(V\) a valuation domain] ⋮ Constructing Gröbner bases for Noetherian rings ⋮ The syzygy theorem for Bézout rings ⋮ A counterexample to the Gröbner ring conjecture ⋮ On syzygy modules over Laurent polynomial rings ⋮ Noncommutative Gröbner Bases over Rings ⋮ Saturation of finitely-generated submodules of free modules over Prüfer domains ⋮ Un Algorithme pour le Calcul des Syzygies surV[X dans le cas oùVest un Domaine de Valuation] ⋮ A zero-dimensional valuation ring is 1-Gröbner

Uses Software

• SINGULAR

Cites Work

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