Averaging algebras, rewriting systems and Gr$\"o$bner-Shirshov bases

DOI10.1142/S021949881850130XarXiv1601.00553MaRDI QIDQ6268955

Publication date: 4 January 2016

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.

Mathematics Subject Classification ID

Applications of universal algebra in computer science (08A70) Grammars and rewriting systems (68Q42) Free algebras (08B20) Centralizing and normalizing extensions (16S20) Gröbner-Shirshov bases (16Z10)

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