Extended letterplace correspondence for nongraded noncommutative ideals and related algorithms

DOI10.1142/S0218196714500519zbMath1329.16039arXiv1206.6027OpenAlexW2109805516MaRDI QIDQ5175606

Roberto La Scala

Publication date: 24 February 2015

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.6027

zbMATH Keywords

free algebrasnoncommutative Gröbner basesnoncommutative algebrasBuchberger algorithmletterplace correspondencegraded commutative algebras

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Graded rings and modules (associative rings and algebras) (16W50) Computational aspects of associative rings (general theory) (16Z05) Software, source code, etc. for problems pertaining to associative rings and algebras (16-04)

Related Items (5)

Monomial right ideals and the Hilbert series of noncommutative modules ⋮ Computing free non-commutative Gröbner bases over \(\mathbb{Z}\) with \textsc{Singular:Letterplace} ⋮ Computing minimal free resolutions of right modules over noncommutative algebras ⋮ Multigraded Hilbert series of noncommutative modules ⋮ Gröbner bases and gradings for partial difference ideals

Uses Software

• Magma
• Maple
• SINGULAR

Cites Work

• Noetherian quotients of the algebra of partial difference polynomials and Gröbner bases of symmetric ideals
• Computing inhomogeneous Gröbner bases
• Letterplace ideals and non-commutative Gröbner bases.
• The diamond lemma for ring theory
• The Magma algebra system. I: The user language
• Skew polynomial rings, Gröbner bases and the letterplace embedding of the free associative algebra.
• Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems
• Equivariant Gröbner bases and the Gaussian two-factor model
• Finite generation of symmetric ideals
• GRÖBNER-SHIRSHOV BASES: SOME NEW RESULTS
• On the Foundations of Combinatorial Theory: IX Combinatorial Methods in Invariant Theory
• Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134)
• Gröbner bases and gradings for partial difference ideals
• Ordering by Divisibility in Abstract Algebras
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