Essential Properties of Admissible Orderings on Differential Monomials
by
Alexey Zobnin
Moscow State University

Admissible monomial orderings play an important role in the construction of Groebner bases of polynomial ideals. In the case of rings of differential polynomials the generalizations of the Groebner-bases technique also demand the specification of an admissible ranking on differential variables or monomials.

Various requirements for those rankings and orderings concerning different methods are considered in this article. We examine some links between those requirements and look at the general properties of admissible differential orderings.

In particular, we show that any admissible ordering well-orders the set of differential monomials. We prove this fact using only three natural and essential axioms, unlike the works of V. Weispfenning, where additional axioms were needed.

Date received: January 29, 2003