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- Title
Averaging algebras, rewriting systems and Gröbner–Shirshov bases.
- Authors
Gao, Xing; Zhang, Tianjie
- 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.
- Subjects
UNITARY operators; AVERAGING principle; POLYNOMIALS; SET theory; AVERAGING method (Differential equations)
- Publication
Journal of Algebra & Its Applications, 2018, Vol 17, Issue 7, pN.PAG
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S021949881850130X