Abelian extension
In abstract algebra, an abelian extension is a Galois extension whose Galois group is abelian. When the Galois group is also cyclic, the extension is also called a cyclic extension. Going in the other direction, a Galois extension is called solvable if its Galois group is solvable, i.e., if the group can be decomposed into a series of normal extensions of an abelian group. Every finite extension of a finite field is a cyclic extension.
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AbelianAbelian ExtensionAbelian extensionsAbsolute Galois groupAlbert–Brauer–Hasse–Noether theoremAlgebraic number fieldAlgebraic number theoryArtin reciprocity lawArtin–Schreier curveArtin–Schreier theoryBasic Number TheoryBiquadratic fieldBirch and Swinnerton-Dyer conjectureBrumer–Stark conjectureCasus irreducibilisChebotarev's density theoremClass field theoryClass formationClass number formulaComplex multiplicationConductor (class field theory)Cyclic (mathematics)Cyclic algebraCyclic extensionCyclic field extensionCyclic groupCyclotomic extensionCyclotomic fieldDedekind zeta functionElliptic unitEmmy NoetherFactor systemField (mathematics)Field extensionGaussian rationalGenus fieldGlossary of areas of mathematicsGroup cohomologyHasse norm theoremHasse–Arf theorem
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Abelian extension
In abstract algebra, an abelian extension is a Galois extension whose Galois group is abelian. When the Galois group is also cyclic, the extension is also called a cyclic extension. Going in the other direction, a Galois extension is called solvable if its Galois group is solvable, i.e., if the group can be decomposed into a series of normal extensions of an abelian group. Every finite extension of a finite field is a cyclic extension.
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Em álgebra abstrata, uma exten ...... o primeiro grupo de homologia.
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En algèbre générale, plus préc ...... ie du corps de classes local).
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En álgebra abstracta, una exte ...... on el primer grupo homológico.
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Im mathematischen Teilgebiet d ...... eilungskörpern enthalten sind.
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In abstract algebra, an abelia ...... y to the first homology group.
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In de abstracte algebra, een d ...... lden en lokale lichamen/velden
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In matematica, in particolare ...... ensioni abeliane di un campo .
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Inom matematiken är en abelsk ...... p kallas utvidgningen cyklisk.
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Rozszerzenie abelowe – w algeb ...... ię bezpośrednio do pierwszej .
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Абелево расширение поля — расш ...... ого поля является циклическим.
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first
L.V.
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id
C/c027560
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last
Kuz'min
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title
cyclotomic extension
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Em álgebra abstrata, uma exten ...... rpos finitos, e corpos locais.
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En algèbre générale, plus préc ...... ie du corps de classes local).
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En álgebra abstracta, una exte ...... cas sobre cuerpos finitos, y .
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Im mathematischen Teilgebiet d ...... n Körpern und lokalen Körpern.
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In abstract algebra, an abelia ...... e field is a cyclic extension.
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In de abstracte algebra, een d ...... lden en lokale lichamen/velden
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In matematica, in particolare ...... ensioni abeliane di un campo .
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Inom matematiken är en abelsk ...... p kallas utvidgningen cyklisk.
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Rozszerzenie abelowe – w algeb ...... dają rozszerzeniu pośredniemu.
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Абелево расширение поля — расш ...... е Кронекера — Вебера произволь
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label
Abelian extension
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Abelsche Erweiterung
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Abelse uitbreiding
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Abelsk utvidgning
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Estensione abeliana
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Extension abélienne
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Extensión abeliana
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Extensão abeliana
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Rozszerzenie abelowe
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Абелеве розширення
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