Most well-known solution techniques for differential equations exploit symmetry in some
form. Systematic methods have been developed for finding and using symmetries, first …

We prove several basic properties for difference ascending chains, including a necessary
and sufficient condition for an ascending chain to be the characteristic set of its saturation …

The classical assumption of differential algebra, differential elimination theory and formal
integrability theory is that the derivations do commute. This is the standard case arising from …

In this paper we introduce an algebra embedding ι: K〈 X〉→ S from the free associative
algebra K〈 X〉 generated by a finite or countable set X into the skew monoid ring S= P⁎ Σ …

Following the recent survey on Buchberger–Zacharias Theory for monoid rings R [S] over a
unitary effective ring R and an effective monoid S, we propose here a presentation of …

We propose resultant based methods for elimination of indeterminates of skew polynomial
systems. We start with defining the concept of resultant for bivariate skew polynomials by …

Ritt-Wu's characteristic set method for ordinary difference polynomial systems with arbitrary
ordering Page 1 Acta Mathematica Scientia 2009,29B(4):1063–1080 http://actams.wipm.ac.cn …

In this paper, a new theory of resolvent systems is developed for prime difference ideals and
difference ideals defined by coherent and proper irreducible ascending chains. Algorithms …

We consider resultant-based methods for elimination of indeterminates of Ore polynomial
systems in Ore algebra. We start with defining the concept of resultant for bivariate Ore …

Differential difference algebras, introduced by Mansfield and Szanto, arose naturally from
differential difference equations. In this paper, we investigate the Gelfand–Kirillov dimension …