On the problem of Baer and Kolchin in the Picard-Vessiot theory / Beata Kocel-Cynk, Elżbieta Sowa // W: Algebraic Methods in Dynamical Systems / eds. Teresa Crespo, Zbigniew Hajto. – Warszawa : Instytut ... więcej

On the problem of Baer and Kolchin in the Picard-Vessiot theory / Beata Kocel-Cynk, Elżbieta Sowa // W: Algebraic Methods in Dynamical Systems / eds. Teresa Crespo, Zbigniew Hajto. – Warszawa : Instytut Matematyczny PAN, 2011. – (Banach Center Publications, ISSN 0137-6934 ; 94). – S. 215-220. – Bibliogr. s. 220, Abstr. – Dedicated to Michael Singer on his 60th Birthday. – Mat. konf.: Conference on Algebraic Methods in Dynamical Systems, Będlewo, 16-22.05.2010. – doi: 10.4064/bc94-0-14. – ISBN 978-83-86806-13-3

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 ... więcej

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.