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

Tom 94 / 2011

Beata Kocel-Cynk, Elżbieta Sowa Banach Center Publications 94 (2011), 215-220 MSC: 12Hxx, 01A05. DOI: 10.4064/bc94-0-14


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.


  • Beata Kocel-CynkInstitute of Mathematics
    Cracow University of Technology
    Warszawska 24
    31-155 Kraków, Poland
  • Elżbieta SowaFaculty of Applied Mathematics
    AGH University of Science and Technology
    Al. Mickiewicza 30
    30-059 Kraków, Poland

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