Computing Gröbner bases by FGLM techniques in a non-commutative setting

DOI10.1006/jsco.1999.0415zbMath0996.16033OpenAlexW2095573084MaRDI QIDQ1588032

Miguel Angel Borges-Trenard, Mijail Borges-Quintana, Ferdinando Mora

Publication date: 17 July 2002

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

Full work available at URL: https://semanticscholar.org/paper/4758341533318ea4e6a0f285197443f18c7ca073

zbMATH Keywords

algorithmsGröbner basesfinitely generated free algebrastwisted semigroup rings

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Ordinary and skew polynomial rings and semigroup rings (16S36) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Ideals in associative algebras (16D25) Computational aspects of associative rings (general theory) (16Z05)

Related Items (9)

The Big Mother of all Dualities: Möller Algorithm ⋮ Computing Gröbner bases associated with lattices ⋮ A lattice formulation of the noncommutative F4 procedure ⋮ Complexity of Gröbner basis detection and border basis detection ⋮ PROPERTIES OF COMMUTATIVE ASSOCIATION SCHEMES DERIVED BY FGLM TECHNIQUES ⋮ Gröbner bases and combinatorics for binary codes ⋮ The symmetric group given by a Gröbner basis ⋮ On a Gröbner bases structure associated to linear codes ⋮ Degröbnerization: a political manifesto

Cites Work

• Non-commutative Gröbner bases in algebras of solvable type
• An algorithm for the construction of matrix representations for finitely presented non-commutative algebras
• Relating rewriting techniques on monoids and rings: congruences on monoids and ideals in monoid rings
• Efficient computation of zero-dimensional Gröbner bases by change of ordering
• An introduction to commutative and noncommutative Gröbner bases
• Gröbner bases of ideals defined by functionals with an application to ideals of projective points
• Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems
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