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

Beata Kocel-Cynk; Elżbieta Sowa

Banach Center Publications (2011)

- Volume: 94, Issue: 1, page 215-220
- ISSN: 0137-6934

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topBeata Kocel-Cynk, and Elżbieta Sowa. "On the problem of Baer and Kolchin in the Picard-Vessiot theory." Banach Center Publications 94.1 (2011): 215-220. <http://eudml.org/doc/282559>.

@article{BeataKocel2011,

abstract = {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.},

author = {Beata Kocel-Cynk, Elżbieta Sowa},

journal = {Banach Center Publications},

keywords = {differential Galois theory; Picard-Vessiot theory},

language = {eng},

number = {1},

pages = {215-220},

title = {On the problem of Baer and Kolchin in the Picard-Vessiot theory},

url = {http://eudml.org/doc/282559},

volume = {94},

year = {2011},

}

TY - JOUR

AU - Beata Kocel-Cynk

AU - Elżbieta Sowa

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

JO - Banach Center Publications

PY - 2011

VL - 94

IS - 1

SP - 215

EP - 220

AB - 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.

LA - eng

KW - differential Galois theory; Picard-Vessiot theory

UR - http://eudml.org/doc/282559

ER -

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