This article is cited in 10 papers

Splitting fields and general differential Galois theory

D. V. Trushin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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.
Bibliography: 14 titles.

Keywords: tensor products, constructed fields, differential closure, splitting field, differential Galois group.

UDC: 512.628.2

MSC: Primary 12H05; Secondary 03C60, 12H10

Received: 22.05.2009 and 07.01.2010

DOI: 10.4213/sm7581

 English version: Sbornik: Mathematics, 2010, 201:9, 1323–1353

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