Year: 2016
Type: article
Abstract: In this paper, we prove the following differential analog of the Noether normalization lemma: for every |$d$|-dimensional differential algebraic variety over differentially closed field of zero characteristic there exists a surjective map on to the |$d$|-dimensional affine space. Equivalently, for every integral differential algebra |$A$| over differential field of zero characteristic there exist differentially independent |$b_1, \ldots, b_d$| such that |$A$| is differentially algebraic over subalgebra |$B$| differentially generated by |$b_1, \ldots, b_d$|, and whenever |$\mathfrak{p} \subset B$| is a prime differential ideal, there exists a prime differential ideal |$\mathfrak{q} \subset A$| such that |$\mathfrak{p} = B \cap \mathfrak{q}$|. We also prove the analogous theorem for differential algebraic varieties over the ring of formal power series over an algebraically closed differential field and present some applications to differential equations.
DOI: 10.1093/imrn/rnw275
Author: Gleb Pogudin
Institution: Lomonosov Moscow State University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2194184529