English

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}
}

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24 pages