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Title: Splitting fields and general differential Galois theory

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.

Authors:
 [1]
  1. M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
Publication Date:
OSTI Identifier:
21418068
Resource Type:
Journal Article
Journal Name:
Sbornik. Mathematics
Additional Journal Information:
Journal Volume: 201; Journal Issue: 9; Other Information: DOI: 10.1070/SM2010v201n09ABEH004114; Journal ID: ISSN 1064-5616
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; BIBLIOGRAPHIES; MATHEMATICAL LOGIC; NONLINEAR PROBLEMS; PARTIAL DIFFERENTIAL EQUATIONS; TENSORS; DIFFERENTIAL EQUATIONS; DOCUMENT TYPES; EQUATIONS

Citation Formats

Trushin, Dmitry V. Splitting fields and general differential Galois theory. United States: N. p., 2010. Web. doi:10.1070/SM2010V201N09ABEH004114.
Trushin, Dmitry V. Splitting fields and general differential Galois theory. United States. https://doi.org/10.1070/SM2010V201N09ABEH004114
Trushin, Dmitry V. 2010. "Splitting fields and general differential Galois theory". United States. https://doi.org/10.1070/SM2010V201N09ABEH004114.
@article{osti_21418068,
title = {Splitting fields and general differential Galois theory},
author = {Trushin, Dmitry V},
abstractNote = {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.},
doi = {10.1070/SM2010V201N09ABEH004114},
url = {https://www.osti.gov/biblio/21418068}, journal = {Sbornik. Mathematics},
issn = {1064-5616},
number = 9,
volume = 201,
place = {United States},
year = {Thu Nov 11 00:00:00 EST 2010},
month = {Thu Nov 11 00:00:00 EST 2010}
}