A Differential Analog of the Noether Normalization Lemma. (24th December 2016) - Pogudin, Gleb
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, …, b_d such that A is differentially algebraic over subalgebra B differentially generated by b_1, …, b_d, and whenever p B is a prime differential ideal, there exists a prime differential ideal q A such that p = 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.