Splitting fields and general differential Galois theory

Abstract

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..

33 pages, this version coincides with the published one

Cited by in corpus (7)

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• Unipotent differential algebraic groups as parameterized differential Galois groups
• A Galois-theoretic proof of the differential transcendence of the incomplete Gamma function
• Extensions of differential representations of SL(2) and tori
• Computation of the difference-differential Galois group and differential relations among solutions for a second-order linear difference equation
• Computing differential Galois groups of second-order linear $q$-difference equations
• Computation of the unipotent radical of the differential Galois group for a parameterized second-order linear differential equation