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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc94-0-14,
author = {Beata Kocel-Cynk and El\.zbieta Sowa},
title = {On the problem of Baer and Kolchin in the Picard-Vessiot theory},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {215-220},
zbl = {1252.12003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc94-0-14}
}
Beata Kocel-Cynk; Elżbieta Sowa. On the problem of Baer and Kolchin in the Picard-Vessiot theory. Banach Center Publications, Tome 95 (2011) pp. 215-220. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc94-0-14/