Averaging algebras, rewriting systems and Gr$\"o$bner-Shirshov bases
Rings and Algebras
2016-04-13 v2
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 Grobner-Shirshov bases based on bracketed polynomials. As an application, we give a basis of the free unitary averaging algebra on a non-empty set.
Keywords
Cite
@article{arxiv.1601.00553,
title = {Averaging algebras, rewriting systems and Gr$\"o$bner-Shirshov bases},
author = {Xing Gao and Tianjie Zhang},
journal= {arXiv preprint arXiv:1601.00553},
year = {2016}
}
Comments
24 pages