Dmitry Trushin
Abstract
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The general Galois theory of arbitrary nonlinear partial differential equations is presented in the paper. For each system of differential equations its splitting field and the differential Galois group are defined. The main result is the theorem on the Galois correspondence for normal extensions.
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The general Galois theory of arbitrary nonlinear partial differential equations is presented in the paper. For each system of differential equations its splitting field and the differential Galois group are defined. The main result is the theorem on the Galois correspondence for normal extensions.
Key concepts: Differential Galois theory, Mathematics, Fundamental theorem of Galois theory, Embedding problem, Galois group, Galois extension, Galois module, Galois cohomology