On the problem of Baer and Kolchin in the Picard-Vessiot theory

Beata Kocel-Cynk, and Elżbieta Sowa. "On the problem of Baer and Kolchin in the Picard-Vessiot theory." Banach Center Publications 94.1 (2011): 215-220. <http://eudml.org/doc/282559>.

@article{BeataKocel2011,
abstract = {We present the history of the development of Picard-Vessiot theory for linear ordinary differential equations. We are especially concerned with the condition of not adding new constants, pointed out by R. Baer. We comment on Kolchin's condition of algebraic closedness of the subfield of constants of the given differential field over which the equation is defined. Some new results concerning existence of a Picard-Vessiot extension for a homogeneous linear ordinary differential equation defined over a real differential field K with real closed field of constants F are also mentioned.},
author = {Beata Kocel-Cynk, Elżbieta Sowa},
journal = {Banach Center Publications},
keywords = {differential Galois theory; Picard-Vessiot theory},
language = {eng},
number = {1},
pages = {215-220},
title = {On the problem of Baer and Kolchin in the Picard-Vessiot theory},
url = {http://eudml.org/doc/282559},
volume = {94},
year = {2011},
}

TY - JOUR
AU - Beata Kocel-Cynk
AU - Elżbieta Sowa
TI - On the problem of Baer and Kolchin in the Picard-Vessiot theory
JO - Banach Center Publications
PY - 2011
VL - 94
IS - 1
SP - 215
EP - 220
AB - We present the history of the development of Picard-Vessiot theory for linear ordinary differential equations. We are especially concerned with the condition of not adding new constants, pointed out by R. Baer. We comment on Kolchin's condition of algebraic closedness of the subfield of constants of the given differential field over which the equation is defined. Some new results concerning existence of a Picard-Vessiot extension for a homogeneous linear ordinary differential equation defined over a real differential field K with real closed field of constants F are also mentioned.
LA - eng
KW - differential Galois theory; Picard-Vessiot theory
UR - http://eudml.org/doc/282559
ER -