Splitting fields and general differential Galois theory

Details Splitting fields and general differential Galois theory Splitting fields and general differential Galois theory

2009-06-05

arxiv.org/abs/0906.1176v2

Sbornik: Mathematics, 201:9 (2010) 1323--1353

Mathematics

Commutative Algebra

33 pages, this version coincides with the published one

Scientific paper

10.1070/SM2010v201n09ABEH004114

An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations. The algebraic technique is based on the search for prime differential ideals of special form in tensor products of differential rings. The main results demonstrating the work of the technique obtained are the theorem on the constructedness of the differential closure and the general theorem on the Galois correspondence for normal extensions..

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