no. 5-6
Algebra
Constrained extensions of real type
[Extensions contraintes de type réel]

Présenté par : Jean-Pierre Serre

Crespo, Teresa1 ; Hajto, Zbigniew2 ; Sowa, Elżbieta3
1 Departament dʼÀlgebra i Geometria, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
2 Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348 Kraków, Poland
3 Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland
Comptes Rendus. Mathématique, Tome 350 (2012) no. 5-6, pp. 235-237.

Nous donnons un théorème dʼexistence pour des extensions de type Picard–Vessiot sur un corps différentiel réel dont le corps des constantes est réel clos.

We present an existence theorem for Picard–Vessiot extensions over real differential fields with real closed field of constants.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.03.006
Crespo, Teresa 1 ; Hajto, Zbigniew 2 ; Sowa, Elżbieta 3

1 Departament dʼÀlgebra i Geometria, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
2 Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348 Kraków, Poland
3 Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland 
@article{CRMATH_2012__350_5-6_235_0,
     author = {Crespo, Teresa and Hajto, Zbigniew and Sowa, El\.zbieta},
     title = {Constrained extensions of real type},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {235--237},
     publisher = {Elsevier},
     volume = {350},
     number = {5-6},
     year = {2012},
     doi = {10.1016/j.crma.2012.03.006},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2012.03.006/}
}
TY  - JOUR
AU  - Crespo, Teresa
AU  - Hajto, Zbigniew
AU  - Sowa, Elżbieta
TI  - Constrained extensions of real type
JO  - Comptes Rendus. Mathématique
PY  - 2012
SP  - 235
EP  - 237
VL  - 350
IS  - 5-6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2012.03.006/
DO  - 10.1016/j.crma.2012.03.006
LA  - en
ID  - CRMATH_2012__350_5-6_235_0
ER  - 
%0 Journal Article
%A Crespo, Teresa
%A Hajto, Zbigniew
%A Sowa, Elżbieta
%T Constrained extensions of real type
%J Comptes Rendus. Mathématique
%D 2012
%P 235-237
%V 350
%N 5-6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2012.03.006/
%R 10.1016/j.crma.2012.03.006
%G en
%F CRMATH_2012__350_5-6_235_0
Crespo, Teresa; Hajto, Zbigniew; Sowa, Elżbieta. Constrained extensions of real type. Comptes Rendus. Mathématique, Tome 350 (2012) no. 5-6, pp. 235-237. doi : 10.1016/j.crma.2012.03.006. http://www.numdam.org/articles/10.1016/j.crma.2012.03.006/

[1] Gelʼfond, O.A.; Khovanskii, A.G. Real Liouville functions, Funktsional. Anal. i Prilozhen., Volume 14 (1980) no. 2, pp. 52-53

[2] Gillet, H.; Gorchinskiy, S.; Ovchinnikov, A. Parameterized Picard–Vessiot extensions and Atiyah extensions | arXiv

[3] Kolchin, E.R. Differential Algebra and Algebraic Groups, Academic Press, 1973

[4] Kolchin, E.R. Constrained extensions of differential fields, Adv. Math., Volume 12 (1974), pp. 141-170

[5] Michaux, C. Some results on ordered differential fields with elimination of quantifiers, Seminarber., Sekt. Math., vol. 93, Humboldt Univ., Berlin, 1987, pp. 142-163

[6] Singer, M.F. A class of differential fields with minimal differential closures, Proc. Amer. Math. Soc., Volume 69 (1978), pp. 319-322

Cité par Sources :