Short notes

General differential Galois theory

D. V. Trushin

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The general Galois theory of 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 words: tensor products, constructed fields, differential closure, splitting fields, differential Galois group.

UDC: 512.628.2

Received: 02.09.2009

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