GRÖBNER-SHIRSHOV BASES: SOME NEW RESULTS

DOI10.1142/9789812790019_0003zbMath1207.16023arXiv0804.1344OpenAlexW2963202507MaRDI QIDQ3620743

Yuqun Chen, Leonid A. Bokut'

Publication date: 14 April 2009

Published in: Advances in Algebra and Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.1344

zbMATH Keywords

modulesLie algebrasHNN-extensionsGröbner-Shirshov basesChinese monoidscomposition-diamond lemmadialgebrasSchreier extensions

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Generators, relations, and presentations of groups (20F05) Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Free semigroups, generators and relations, word problems (20M05) Identities, free Lie (super)algebras (17B01) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Computational aspects of associative rings (general theory) (16Z05)

Related Items (20)

Gröbner-Shirshov bases for some Lie algebras ⋮ Finite presentability of generalized Bruck–Reilly ∗-extension of groups ⋮ Unnamed Item ⋮ Gröbner-Shirshov bases for extended modular, extended Hecke, and Picard groups. ⋮ Gröbner-Shirshov bases for semirings. ⋮ Gröbner-Shirshov bases for free Gelfand-Dorfman-Novokov algebras and for right ideals of free right Leibniz algebras ⋮ Gröbner–Shirshov basis method for multiple tensor products of some associative algebras ⋮ Gröbner-Shirshov bases for Lie algebras over a commutative algebra ⋮ Gröbner-Shirshov bases for Vinberg-Koszul-Gerstenhaber right-symmetric algebras ⋮ New approaches to plactic monoid via Gröbner-Shirshov bases. ⋮ Gröbner-Shirshov basis for the singular part of the Brauer semigroup ⋮ Gröbner-Shirshov bases for metabelian Lie algebras ⋮ Gröbner–Shirshov bases and their calculation ⋮ A new Composition-Diamond lemma for associative conformal algebras ⋮ Extended letterplace correspondence for nongraded noncommutative ideals and related algorithms ⋮ Composition-diamond lemma for tensor product of free algebras. ⋮ INTERNET SECURITY APPLICATIONS OF GRÖBNER-SHIRSHOV BASES ⋮ Gröbner–Shirshov bases for commutative dialgebras ⋮ Gröbner-Shirshov bases for associative algebras with multiple operators and free Rota-Baxter algebras. ⋮ Gröbner-Shirshov Bases of the Generalized Bruck-Reilly ∗-Extension

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