Splitting fields and general differential Galois theory

Journal Article · Thu Nov 11 00:00:00 EST 2010 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2010V201N09ABEH004114· OSTI ID:21418068

Trushin, Dmitry V ^[1]

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1. M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

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.

• OSTI ID: 21418068
• Journal Information: Sbornik. Mathematics, Vol. 201, Issue 9; Other Information: DOI: 10.1070/SM2010v201n09ABEH004114; ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
BIBLIOGRAPHIES
MATHEMATICAL LOGIC
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
TENSORS
DIFFERENTIAL EQUATIONS
DOCUMENT TYPES
EQUATIONS