Submission date: 21 January 2009.

Abstract:

We give a characterization of existentially closed partial differential fields (i.e. fields equipped with finitely many commuting derivations and an automorphism) in terms of differential varieties. We use the latter to obtain several algebraic results on these fields (e.g. we prove a Nullstellensatz Theorem in this context) and the particular subfields of constants and fixed points.

Mathematics Subject Classification: 03C65 ,53.99

Keywords and phrases: partial differential field with an automorphism

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