Rédaction n°046. Algèbre. Chapitre VI. Corps commutatifs, précédé de commentaires. (état 1).
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Commentaire à l'appendice au chapitre V ainsi qu'au chapitre VI, puis chapitre VI à proprement parler. § 1. Caractéristique, corps premiers. § 2. Extensions simples. Eléments algébriques et éléments transcendants. § 3. Extensions algébriques et extensions transcendantes. § 4. Extensions algébriquement stables. § 5. Isomorphismes d'extensions algébriques. § 6. Extensions galoisiennes. § 7. Racines de l'unité, corps finis. § 8. Corps ordonnés et corps quasi-réels. § 9. Divisibilité dans les extensions algébriques. Appendice I. Extensions galoisiennes infinies. Appendice II. Extensions algébriques des corps p-adiques.
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R046_iecnr055
Rédaction n°047. Algèbre. Théorie des corps commutatifs (état 2).
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=corps+commutatifs">corps commutatifs</a>
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<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=extensions+normales">extensions normales</a>
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=extensions+galoisiennes">extensions galoisiennes</a>
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=groupes+de+Galois">groupes de Galois</a>
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=racines+de+l%27unit%C3%A9">racines de l'unité</a>
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<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=extensions+transcendantes">extensions transcendantes</a>
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=extensions+compos%C3%A9es">extensions composées</a>
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§ 1. La caractéristique. Corps premiers. § 2. Extensions algébriques. § 3. Corps algébriquement fermés. § 4. Extensions normales. § 5. La théorie de Galois. § 6. Extensions algébriques séparables. § 7. Racines de l'unité. Corps finis. § 8. Extensions finies considérées comme algèbres. § 9. Bases de transcendance. § 10. Extensions composées. § 11. Extensions séparables. § 12. Corps relativement algébriquement fermés.
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=39&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=Chevalley%2C+Claude">Chevalley, Claude</a>
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R047_iecnr056
Rédaction n°099. Algèbre. Chapitre V. Corps commutatifs (état 3)
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=corps+commutatifs">corps commutatifs</a>
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=extensions+alg%C3%A9briques">extensions algébriques</a>
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=extensions+transcendantes">extensions transcendantes</a>
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=corps+alg%C3%A9briquement+clos">corps algébriquement clos</a>
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=extensions+s%C3%A9parables">extensions séparables</a>
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=extensions+normales">extensions normales</a>
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=extensions+galoisiennes">extensions galoisiennes</a>
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=groupes+de+Galois">groupes de Galois</a>
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=racines+de+l%27unit%C3%A9">racines de l'unité</a>
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<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=extensions+cycliques">extensions cycliques</a>
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§ 1. Corps premiers. Caractéristique. § 2. Extensions algébriques et extensions transcendantes. § 3. Corps algébriquement fermés. Extensions universelles. § 4. Isomorphismes. Dérivations. Extensions séparables. § 5. Composition des corps. § 6. Extensions normales. Théorie de Galois. § 7. Racines de l'unité. Corps finis. § 8. Extensions cycliques. La rédaction s'achève sur un appendice consacré aux extensions normales de degré infini.
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R099_nbr010
Rédaction n°109. Algèbre. Chapitre V. Corps commutatifs (état 4)
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=corps+commutatifs">corps commutatifs</a>
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<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=extensions+transcendantes">extensions transcendantes</a>
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=extensions+compos%C3%A9es">extensions composées</a>
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=extensions+s%C3%A9parables">extensions séparables</a>
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=extensions+galoisiennes">extensions galoisiennes</a>
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=groupes+de+Galois">groupes de Galois</a>
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=racines+de+l%27unit%C3%A9">racines de l'unité</a>
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=corps+finis">corps finis</a>
<a href="/items/browse?advanced%5B0%5D%5Belement_id%5D=49&advanced%5B0%5D%5Btype%5D=is+exactly&advanced%5B0%5D%5Bterms%5D=extensions+cycliques">extensions cycliques</a>
§ 1. Corps premiers. Caractéristique. § 2. Extensions. § 3. Extensions algébriques. § 4. Extensions transcendantes. § 5. Extensions composées. § 6. Théorème d'existence. § 7. Isomorphismes. Dérivations - séparabilité. § 8. Théorie de Galois. § 9. Exemples : Racines de l'unité, corps finis, extensions cycliques.
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R109_nbr019