FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2003, VOLUME 9, NUMBER 3, PAGES 89-102

**On standard bases in rings of differential polynomials**

A. I. Zobnin

Abstract

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We consider Ollivier's standard bases (also known as differential
Gröbner 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 $[xp]$ has
a finite standard basis (w.r.t.
the so-called $$b-orderings) that
contains only one element.
Various properties of admissible orderings on differential monomials
are studied.
We bring up the following problem: whether there is a finitely
generated differential ideal that does not admit a finite
standard basis w.r.t.
any ordering.

Location: http://mech.math.msu.su/~fpm/eng/k03/k033/k03306h.htm.

Last modified: January 24, 2005.