CONSTRUCTION OF FREE COMMUTATIVE INTEGRO-DIFFERENTIAL ALGEBRAS BY THE METHOD OF GRÖBNER–SHIRSHOV BASES

DOI10.1142/S0219498813501600zbMath1317.16022arXiv1302.0041OpenAlexW2963012035MaRDI QIDQ5420511

Xing Gao, Shanghua Zheng, Li Guo

Publication date: 13 June 2014

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.0041

zbMATH Keywords

free algebrasGröbner-Shirshov basesRota-Baxter algebrasintegro-differential algebrascomposition-diamond lemmadifferential algebrasmixable shuffle products

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Derivations and commutative rings (13N15) Differential algebra (12H05)

Related Items (13)

Averaging algebras, rewriting systems and Gröbner–Shirshov bases ⋮ Algorithmic operator algebras via normal forms in tensor rings ⋮ On integro-differential algebras. ⋮ Construction of free commutative Reynolds algebras by Gröbner-Shirshov bases ⋮ Free weighted (modified) differential algebras, free (modified) Rota–Baxter algebras and Gröbner–Shirshov bases ⋮ On rings of differential Rota–Baxter operators ⋮ Free integro-differential algebras and Gröbner-Shirshov bases. ⋮ Constructions of Free Commutative Integro-Differential Algebras ⋮ Gröbner–Shirshov bases and their calculation ⋮ Free (tri)dendriform family algebras ⋮ Free nonunitary Rota-Baxter family algebras and typed leaf-spaced decorated planar rooted forests ⋮ Free Rota-Baxter family algebras and (tri)dendriform family algebras ⋮ An algebraic study of Volterra integral equations and their operator linearity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Gröbner-Shirshov bases for Rota-Baxter algebras.
• An analytic problem whose solution follows from a simple algebraic identity
• What is a classical r-matrix?
• Solving and factoring boundary problems for linear ordinary differential equations in differential algebras
• Renormalization of multiple zeta values
• Composition-diamond lemma for tensor product of free algebras.
• Operated semigroups, Motzkin paths and rooted trees
• Gröbner-Shirshov bases for associative algebras with multiple operators and free Rota-Baxter algebras.
• The diamond lemma for ring theory
• Differential type operators and Gröbner-Shirshov bases.
• Baxter algebras and shuffle products
• Quasi-shuffle products
• On free Baxter algebras: Completions and the internal construction
• On differential Rota-Baxter algebras.
• Mixable shuffles, quasi-shuffles and Hopf algebras.
• On the structure of free Baxter algebras
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• Gröbner-Shirshov Bases for Categories
• Spitzer's identity and the algebraic Birkhoff decomposition in pQFT
• Term Rewriting and All That
• A unified algebraic approach to the classical Yang–Baxter equation
• Baxter algebras and combinatorial identities. I

This page was built for publication: CONSTRUCTION OF FREE COMMUTATIVE INTEGRO-DIFFERENTIAL ALGEBRAS BY THE METHOD OF GRÖBNER–SHIRSHOV BASES