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- Title
CONSTRUCTION OF FREE COMMUTATIVE INTEGRO-DIFFERENTIAL ALGEBRAS BY THE METHOD OF GRÖBNER-SHIRSHOV BASES.
- Authors
GAO, XING; GUO, LI; ZHENG, SHANGHUA
- Abstract
In this paper, we construct free commutative integro-differential algebras by applying the method of Gröbner-Shirshov bases. We establish the Composition-Diamond Lemma for free commutative differential Rota-Baxter (DRB) algebras of order n. We also obtain a weakly monomial order on these algebras, allowing us to obtain Gröbner-Shirshov bases for free commutative integro-differential algebras on a set. We finally generalize the concept of functional monomials to free differential algebras with arbitrary weight and generating sets from which to construct a canonical linear basis for free commutative integro-differential algebras.
- Subjects
COMMUTATIVE rings; INTEGRO-differential equations; DIFFERENTIAL algebra; ALGEBRAIC fields; FREE algebras; ALGEBRAIC field theory; ALGEBRAIC functions
- Publication
Journal of Algebra & Its Applications, 2014, Vol 13, Issue 5, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498813501600