Gao, Xing, Guo, Li, Rosenkranz, Markus (2014) Free integrodifferential algebras and GroebnerShirshov bases. Journal of Algebra, 442 . pp. 354396. ISSN 00218693. (doi:10.1016/j.jalgebra.2014.10.016) (KAR id:43407)
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Official URL: http://dx.doi.org/10.1016/j.jalgebra.2014.10.016 
Abstract
The notion of commutative integrodifferential algebra was introduced for the algebraic study of boundary problems for linear ordinary differential equations. Its noncommutative analog achieves a similar purpose for linear systems of such equations. In both cases, free objects are crucial for analyzing the underlying algebraic structures, e.g. of the (matrix) functions.
In this paper we apply the method of GroebnerShirshov bases to construct the free (noncommutative) integrodifferential algebra on a set. The construction is from the free RotaBaxter algebra on the free differential algebra on the set modulo the differential RotaBaxter ideal generated by the noncommutative integration by parts formula. In order to obtain a canonical basis for this quotient, we first reduce to the case when the set is finite. Then in order to obtain the monomial order needed for the CompositionDiamond Lemma, we consider the free RotaBaxter algebra on the truncated free differential algebra. A CompositionDiamond Lemma is proved in this context, and a GroebnerShirshov basis is found for the corresponding differential RotaBaxter ideal.
Item Type:  Article 

DOI/Identification number:  10.1016/j.jalgebra.2014.10.016 
Additional information:  Available online before print 
Uncontrolled keywords:  RotaBaxter algebras; integrodifferential algebras; integrodifferential equations; noncommutative algebras; free objects. 
Subjects: 
Q Science > QA Mathematics (inc Computing science) > QA150 Algebra Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations 
Divisions:  Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science 
Funders:  [UNSPECIFIED] EPSRC 
Depositing User:  Markus Rosenkranz 
Date Deposited:  15 Oct 2014 09:02 UTC 
Last Modified:  16 Feb 2021 12:56 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/43407 (The current URI for this page, for reference purposes) 
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