Free weighted (modified) differential algebras, free (modified) Rota-Baxter algebras and Gr\"{o}bner-Shirshov bases
Zhicheng Zhu, Huhu Zhang, Xing Gao
TL;DR
This paper develops new linear bases for free weighted differential and Rota-Baxter algebras using Gr"{o}bner-Shirshov bases, advancing algebraic structure understanding.
Contribution
It introduces novel linear bases for free (modified) weighted differential and Rota-Baxter algebras via Gr"{o}bner-Shirshov bases methodology.
Findings
New linear bases for free weighted differential algebras
New linear bases for free modified Rota-Baxter algebras
Application of Gr"{o}bner-Shirshov bases in algebraic basis construction
Abstract
In this paper, we obtain respectively some new linear bases of free unitary (modified) weighted differential algebras and free nonunitary (modified) Rota-Baxter algebras, in terms of the method of Gr\"{o}bner-Shirshov bases.
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