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Comptes Rendus Mathématique
Volume 348, n° 9-10
pages 487-490 (mai 2010)
Doi : 10.1016/j.crma.2010.04.004
Received : 12 February 2009 ;  accepted : 6 April 2010
Differential ‘Galois’ extensions with new constants
Extensions différentielles « galoisiennes » avec nouvelles constantes
 

Lourdes Juan a , Andy R. Magid b
a Department of Mathematics, Texas Tech University, Lubbock, TX 79409, United States 
b Department of Mathematics, University of Oklahoma, Norman, OK 73019, United States 

Abstract

Let F be a differential field with algebraically closed field of constants   and let E be a differential field extension of F . The field E is a differential Galois extension if it is generated over F by a full set of solutions of a linear homogeneous differential equation with coefficients in F and if its field of constants coincides with  . We study the differential field extensions of F that satisfy the first condition but not the second.

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Résumé

Soit F un corps différentiel dont le corps des constantes   est algébriquement clos et soit   une extension de corps différentiels. Le corps différentiel E est une extension galoisienne différentielle de F s’il est engendré sur F par une base de solutions d’une équation différentielle linéaire homogène à coefficients dans F et si son corps des constantes est  . Nous étudions les extensions différentielles de F qui satisfont la première condition et non la seconde.

The full text of this article is available in PDF format.


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