Geodesic
Differential standard bases under composition
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 1, pp. 109-134

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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 $\mathcal F\{y\}$. 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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     author = {A. I. Zobnin},
     title = {Differential standard bases under composition},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {109--134},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2007_13_1_a6/}
}
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A. I. Zobnin. Differential standard bases under composition. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 1, pp. 109-134. http://geodesic.mathdoc.fr/item/FPM_2007_13_1_a6/