Dissociation des Extensions Algébriques de Corps par les Extensions Galoisiennes ou Galsimples non Galoisiennes

Abstract : The fundamental Theorem of Arithmetic factorizes any integer in a product of prime numbers. The Jordan-Hölder Theorem unravels many groups by their normal series which are refined in composition series. The central topic of this thesis is the dissociation of field extensions. We dissociate algebraic extensions by their intermediate fields in order to construct a tower with maximum number of Galois steps. We say that an algebraic extension is "galtourables" if it dissociates into a Galois tower (all steps of which are Galois extensions). Two Galois towers of the same galtowerable extension (finite or infinite) admit equivalent refinements. But there exist nongaltowerable algebraic extensions. Into any finite extension, there is a unique intermediate field, no extension of which is galtowerable : its "field of intowerability".Then, we say that the ultimate step of an "elevation tower" of a nongaltowerable extension is "galsimple" ; and it is nonGalois. The final theorem of this thesis dissociates any finite extension by its elevation towers which are refined in "composition towers". Thus we obtain an analogue, for fields extensions, to the Jordan-Hölder Theorem for groups.
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Theses
Mathematics. Université de Valenciennes et du Hainaut-Cambresis, 2004. French


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Submitted on : Monday, January 10, 2005 - 3:28:42 PM
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Emmanuel Andréo. Dissociation des Extensions Algébriques de Corps par les Extensions Galoisiennes ou Galsimples non Galoisiennes. Mathematics. Université de Valenciennes et du Hainaut-Cambresis, 2004. French. <tel-00007720>

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