naa a22 4500 510782205 CHVBK 20180411083251.0 cr unu---uuuuu 180411e20131101xx s 000 0 eng 10.1007/s11856-013-0015-x doi (NATIONALLICENCE)springer-10.1007/s11856-013-0015-x Picard-Vessiot theory for real fields [Elektronische Daten] [Teresa Crespo, Zbigniew Hajto, Elżbieta Sowa] The existence of a Picard-Vessiot extension for a homogeneous linear differential equation has been established when the differential field over which the equation is defined has an algebraically closed field of constants. In this paper, we prove the existence of a Picard-Vessiot extension for a homogeneous linear differential equation defined over a real differential field K with real closed field of constants. We give an adequate definition of the differential Galois group of a Picard-Vessiot extension of a real differential field with real closed field of constants and we prove a Galois correspondence theorem for such a Picard-Vessiot extension. Hebrew University Magnes Press, 2013 Crespo Teresa Departament d' Àlgebra i Geometria, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007, Barcelona, Spain aut Hajto Zbigniew Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348, Kraków, Poland aut Sowa Elżbieta Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059, Kraków, Poland aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 198/1(2013-11-01), 75-89 0021-2172 198:1<75 2013 198 11856 https://doi.org/10.1007/s11856-013-0015-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-013-0015-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Crespo Teresa Departament d' Àlgebra i Geometria, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007, Barcelona, Spain aut NATIONALLICENCE 700 1- Hajto Zbigniew Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348, Kraków, Poland aut NATIONALLICENCE 700 1- Sowa Elżbieta Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059, Kraków, Poland aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 198/1(2013-11-01), 75-89 0021-2172 198:1<75 2013 198 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer