From algebra to analysis: New proofs of theorems by Ritt and Seidenberg

Pavlov, D.; Pogudin, G.; Razmyslov, Yu.

doi:10.1090/proc/16065

From algebra to analysis: New proofs of theorems by Ritt and Seidenberg
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by D. Pavlov, G. Pogudin and Yu. P. Razmyslov PDF

Proc. Amer. Math. Soc. 150 (2022), 5085-5095 Request permission

Abstract:

Ritt’s theorem of zeroes and Siedenberg’s embedding theorem are classical results in differential algebra allowing to connect algebraic and model-theoretic results on nonlinear PDEs to the realm of analysis. However, the existing proofs of these results use sophisticated tools from constructive algebra (characteristic set theory) and analysis (Riquier’s existence theorem).

In this paper, we give new short proofs for both theorems relying only on basic facts from differential algebra and the classical Cauchy-Kovalevskaya theorem for PDEs.

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