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

• Autorzy: Beata Kocel-Cynk , Elżbieta Sowa
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 01A05: General histories, source books
• 12Hxx: Differential and difference algebra

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 94
• Numer: 1
• Strony: 215-220

Daty

wydano

2011

Twórcy

autor

Beata Kocel-Cynk

• Institute of Mathematics, Cracow University of Technology, Warszawska 24, 31-155 Kraków, Poland

autor

Elżbieta Sowa

• Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland

Identyfikatory

DOI

10.4064/bc94-0-14