# Wydawnictwa / Banach Center Publications / Wszystkie tomy

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

### Tom 94 / 2011

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

#### Streszczenie

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.

#### Autorzy

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

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