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.
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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@article{CRMATH_2010__348_9-10_487_0, author = {Juan, Lourdes and Magid, Andy R.}, title = {Differential {{\textquoteleft}Galois{\textquoteright}} extensions with new constants}, journal = {Comptes Rendus. Math\'ematique}, pages = {487--490}, publisher = {Elsevier}, volume = {348}, number = {9-10}, year = {2010}, doi = {10.1016/j.crma.2010.04.004}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2010.04.004/} }
TY - JOUR AU - Juan, Lourdes AU - Magid, Andy R. TI - Differential ‘Galois’ extensions with new constants JO - Comptes Rendus. Mathématique PY - 2010 SP - 487 EP - 490 VL - 348 IS - 9-10 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2010.04.004/ DO - 10.1016/j.crma.2010.04.004 LA - en ID - CRMATH_2010__348_9-10_487_0 ER -
%0 Journal Article %A Juan, Lourdes %A Magid, Andy R. %T Differential ‘Galois’ extensions with new constants %J Comptes Rendus. Mathématique %D 2010 %P 487-490 %V 348 %N 9-10 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2010.04.004/ %R 10.1016/j.crma.2010.04.004 %G en %F CRMATH_2010__348_9-10_487_0
Juan, Lourdes; Magid, Andy R. Differential ‘Galois’ extensions with new constants. Comptes Rendus. Mathématique, Tome 348 (2010) no. 9-10, pp. 487-490. doi : 10.1016/j.crma.2010.04.004. http://archive.numdam.org/articles/10.1016/j.crma.2010.04.004/
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