Computational ideal theory in finitely generated extension rings

DOI10.1016/S0304-3975(00)00172-9zbMath0945.68197OpenAlexW2138402185MaRDI QIDQ1575702

Joachim Apel

Publication date: 21 August 2000

Published in: Theoretical Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0304-3975(00)00172-9

zbMATH Keywords

Gröbner bases

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Nonnumerical algorithms (68W05) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10)

Related Items

Buchberger-Weispfenning theory for effective associative rings ⋮ Letterplace ideals and non-commutative Gröbner bases. ⋮ Computing free non-commutative Gröbner bases over \(\mathbb{Z}\) with \textsc{Singular:Letterplace} ⋮ Non-associative Gröbner bases ⋮ Buchberger-Zacharias theory of multivariate Ore extensions ⋮ Differential algebra for derivations with nontrivial commutation rules ⋮ Looking for Gröbner basis theory for (almost) skew 2-nomial algebras. ⋮ Toward involutive bases over effective rings ⋮ Effective Buchberger-Zacharias-Weispfenning theory of skew polynomial extensions of subbilateral coherent rings ⋮ Zacharias representation of effective associative rings ⋮ Why you cannot even hope to use Ore algebras in cryptography ⋮ Weight ideals associated to regular and log-linear arrays. ⋮ Degree bounds for Gröbner bases in algebras of solvable type ⋮ A primer on ideal theoretical operation in non-commutative polynomial rings ⋮ De nugis Groebnerialium 6: Rump, Ufnarovski, Zacharias

Uses Software

• Felix

Cites Work

• Non-commutative Gröbner bases in algebras of solvable type
• On the construction of Gröbner bases using syzygies
• On the theory of graded structures
• New constructive methods in classical ideal theory
• A generalization of reduction rings
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• Über B. Buchbergers Verfahren, Systeme algebraischer Gleichungen zu lösen
• An algorithm for constructing Gröbner and free Schreier bases in free group algebras
• A generalization of Gröbner basis algorithms to polycyclic group rings
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
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