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Статья

Differential standard bases under composition

Journal of Mathematical Sciences. 2008. Vol. 152. No. 4. P. 522-539.

Abstract. We generalize Hoon Hong’s theorem on Gr¨obner bases under composition to the case of differential standard bases in the ordinary ring of differential polynomials 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.