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Averaging algebras, rewriting systems and Gröbner–Shirshov bases

School of Mathematics and Statistics, Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, P. R. China

E-mail Address: gaoxing@lzu.edu.cn

Corresponding author.

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and

Tianjie Zhang

School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, P. R. China

School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P. R. China

E-mail Address: 907105216@qq.com

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https://doi.org/10.1142/S021949881850130XCited by:5 (Source: Crossref)

Abstract

In this paper, we study the averaging operator by assigning a rewriting system to it. We obtain some basic results on the kind of rewriting system we used. In particular, we obtain a sufficient and necessary condition for the confluence. We supply the relationship between rewriting systems and Gröbner–Shirshov bases based on bracketed polynomials. As an application, we give a basis of the free unitary averaging algebra on a nonempty set.

Communicated by L. Bokut

Keywords:

AMSC: 08B20, 16R99, 08A70, 16S20

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