(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 $\mathcal F \left\{y\right\}$. 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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