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Article

A Differential Analog of the Noether Normalization Lemma

International Mathematics Research Notices. 2018. Vol. 2018. No. 4. P. 1177-1199.
Pogudin G.

In this paper, we prove the following differential analog of the Noether normalization lemma: for every dd-dimensional differential algebraic variety over differentially closed field of zero characteristic there exists a surjective map on to the dd-dimensional affine space. Equivalently, for every integral differential algebra AA over differential field of zero characteristic there exist differentially independent b1,…,bdb1,…,bd such that AA is differentially algebraic over subalgebra BB differentially generated by b1,…,bdb1,…,bd⁠, and whenever p⊂Bp⊂B is a prime differential ideal, there exists a prime differential ideal q⊂Aq⊂A such that p=B∩qp=B∩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.