FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 1, PAGES 109-134

**Differential standard bases under composition**

A. I. Zobnin

Abstract

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We generalize Hoon Hong's theorem on Gröbner bases under
composition to the case of differential standard bases in the ordinary
ring of differential polynomials $\backslash mathcal\; F\; \{y\}$.
In particular, we prove that some ideals have finite differential
standard bases.
We construct special orderings on differential monomials such that
ideals generated by some power of a quasi-linear polynomial
acquire finite differential standard bases.

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Last modified: December 21, 2006