ON STANDARD BASES IN RINGS OF DIFFERENTIAL POLYNOMIALS

摘要

We consider Ollivier's standard bases (also known as differential Groebner bases) in an ordinary ring of differential polynomials in one indeterminate. We establish a link between these bases and Levi's reduction process. We prove that the ideal [x~p] has a finite standard basis (w.r.t. the so-called β-orderings) that contains only one element. Various properties of admissible orderings on differential monomials are studied. We bring up the question of whether there is a finitely generated differential ideal that does not admit a finite standard basis w.r.t. any ordering.