Picard-Vessiot theory for real fields

被引：0
|
作者：
Teresa Crespo
Zbigniew Hajto
Elżbieta Sowa
机构：
[1] Universitat de Barcelona,Departament d’ Àlgebra i Geometria
[2] Jagiellonian University,Faculty of Mathematics and Computer Science
[3] AGH University of Science and Technology,Faculty of Applied Mathematics
来源：
Israel Journal of Mathematics | 2013年 / 198卷
关键词：
Algebraic Group; Galois Group; Closed Subgroup; Galois Theory; Quadratic Extension;
D O I：
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学科分类号：
摘要：
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.
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页码：75 / 89
页数：14
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