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On differential Galois groups of strongly normal extensions
Author(s) -
Brouette Quentin,
Point Françoise
Publication year - 2018
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201600098
Subject(s) - mathematics , galois group , differential galois theory , fundamental theorem of galois theory , pure mathematics , differential (mechanical device) , embedding problem , galois module , automorphism , galois cohomology , differential algebra , class (philosophy) , galois extension , algebra over a field , computer science , physics , artificial intelligence , thermodynamics
We revisit Kolchin's results on definability of differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed. In certain classes of differential topological fields, which encompasses ordered or p ‐valued differential fields, we find a partial Galois correspondence and we show one cannot expect more in general. In the class of ordered differential fields, using elimination of imaginaries in CODF , we establish a relative Galois correspondence for relatively definable subgroups of the group of differential order automorphisms.