Geodesic
Splitting fields and general differential Galois theory
Sbornik. Mathematics, Tome 201 (2010) no. 9, pp. 1323-1353

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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     author = {D. V. Trushin},
     title = {Splitting fields and general differential {Galois} theory},
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     url = {http://geodesic.mathdoc.fr/item/SM_2010_201_9_a3/}
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D. V. Trushin. Splitting fields and general differential Galois theory. Sbornik. Mathematics, Tome 201 (2010) no. 9, pp. 1323-1353. http://geodesic.mathdoc.fr/item/SM_2010_201_9_a3/