Differential standard bases under composition

A. I. Zobnin

Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 1, pp. 109-134.

Résumé

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 $\mathcal F\{y\}$. 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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