PICARD-VESSIOT THEORY FOR REAL FIELDS

被引：3

作者：

Crespo, Teresa ^{[1
]}

Hajto, Zbigniew ^{[2
]}

Sowa, Elzbieta ^{[3
]}

机构：

[1] Univ Barcelona, Dept Algebra & Geometria, E-08007 Barcelona, Spain

[2] Jagiellonian Univ, Fac Math & Comp Sci, PL-30348 Krakow, Poland

[3] AGH Univ Sci & Technol, Fac Appl Math, PL-30059 Krakow, Poland

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2013年 / 198卷 / 01期

关键词：

DIFFERENTIAL GALOIS THEORY; CONSTRAINED EXTENSIONS; EQUATIONS;

D O I：

10.1007/s11856-013-0015-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：75 / 89

页数：15

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