@incollection{1973121,
    Abstract = {There is no direct analog for differential polynomials of the Hubert basis theorem for polynomials. There is, however, a weakened analog, the basis theorem of Ritt and Raudenbush. In this chapter we prove a very general version of this theorem. The Ritt-Raudenbush theorem and the known generalizations of it are corollaries of the present version. The basis theorem and the lemma on which it is based are applied to the following varied topics: behavior of prime differential polynomial ideals under extension of the differential field of coefficients, differential fields of definition of differential polynomial ideals, universal extensions, and differential specializations. Throughout the chapter denotes a differential ring, and denotes a differential field for the characteristic of which we write p and for the field of constants of which we write . For as well as for we denote the set of derivation operators by Δ, the set of derivative operators by Θ, and the set of derivative operators of order less than or equal to s by Θ(s). The letters y and z, with or without subscripts, stand for differential indeterminates.},
    Editor = {Kolchin, E.R.},
    File = {The Basis Theorem and Some Related Topics - chapter-iii-the-basis-theorem-and-some-related-topics-1973 - a - a - a - a - n.pdf},
    ISSN = {0079-8169},
    Pages = {121 - 144},
    Publisher = {Elsevier},
    Series = {Pure and Applied Mathematics},
    Title = {Chapter III The Basis Theorem and Some Related Topics},
    URL = {http://www.sciencedirect.com/science/article/pii/S007981690862632X},
    Volume = {54},
    Year = {1973},
    bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S007981690862632X},
    bdsk-url-2 = {https://doi.org/10.1016/S0079-8169(08)62632-X},
    date-added = {2020-04-09 14:31:19 +0200},
    date-modified = {2020-04-09 14:31:19 +0200},
    doi = {10.1016/S0079-8169(08)62632-X}
}

@incollection{1973121, Abstract = {There is no direct analog for differential polynomials of the Hubert basis theorem for polynomials. There is, however, a weakened analog, the basis theorem of Ritt and Raudenbush. In this chapter we prove a very general version of this theorem. The Ritt-Raudenbush theorem and the known generalizations of it are corollaries of the present version. The basis theorem and the lemma on which it is based are applied to the following varied topics: behavior of prime differential polynomial ideals under extension of the differential field of coefficients, differential fields of definition of differential polynomial ideals, universal extensions, and differential specializations. Throughout the chapter denotes a differential ring, and denotes a differential field for the characteristic of which we write p and for the field of constants of which we write . For as well as for we denote the set of derivation operators by Δ, the set of derivative operators by Θ, and the set of derivative operators of order less than or equal to s by Θ(s). The letters y and z, with or without subscripts, stand for differential indeterminates.}, Editor = {Kolchin, E.R.}, File = {The Basis Theorem and Some Related Topics - chapter-iii-the-basis-theorem-and-some-related-topics-1973 - a - a - a - a - n.pdf}, ISSN = {0079-8169}, Pages = {121 - 144}, Publisher = {Elsevier}, Series = {Pure and Applied Mathematics}, Title = {Chapter III The Basis Theorem and Some Related Topics}, URL = {http://www.sciencedirect.com/science/article/pii/S007981690862632X}, Volume = {54}, Year = {1973}, bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S007981690862632X}, bdsk-url-2 = {https://doi.org/10.1016/S0079-8169(08)62632-X}, date-added = {2020-04-09 14:31:19 +0200}, date-modified = {2020-04-09 14:31:19 +0200}, doi = {10.1016/S0079-8169(08)62632-X} }