Constrained extensions of real type

Teresa Crespo; Zbigniew Hajto; Elżbieta Sowa

doi:10.1016/j.crma.2012.03.006

Algebra

Constrained extensions of real type
[Extensions contraintes de type réel]

Présenté par : Jean-Pierre Serre

Teresa Crespo ¹ ; Zbigniew Hajto ² ; Elżbieta Sowa 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

Comptes Rendus. Mathématique, Volume 350 (2012) no. 5-6, pp. 235-237.

Résumé
Abstract

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 : 2012-02-09
Accepté le : 2012-03-06
Publié le : 2012-03-01

DOI : 10.1016/j.crma.2012.03.006

Affiliations des auteurs :

Teresa Crespo ¹ ; Zbigniew Hajto ² ; Elżbieta Sowa ³

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     title = {Constrained extensions of real type},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {235--237},
     publisher = {Elsevier},
     volume = {350},
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     year = {2012},
     doi = {10.1016/j.crma.2012.03.006},
     language = {en},
}

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Teresa Crespo; Zbigniew Hajto; Elżbieta Sowa. Constrained extensions of real type. Comptes Rendus. Mathématique, Volume 350 (2012) no. 5-6, pp. 235-237. doi : 10.1016/j.crma.2012.03.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.03.006/

Bibliographie
Cité par

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

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

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

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

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

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

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