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Kummer theory

In abstract algebra and number theory, Kummer theory provides a description of certain types of field extensions involving the adjunction of nth roots of elements of the base field. The theory was originally developed by Ernst Eduard Kummer around the 1840s in his pioneering work on Fermat's Last Theorem. The main statements do not depend on the nature…

Kummer extensions, Kummer map & For elliptic curves

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Overview

Kummer extensions

Kummer map

For elliptic curves

Generalizations

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Kummer theory

Nodes49
Edges48
Triples25
Avg. degree1.96
Density0.040816
Components1

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Kummer theory

Top relations

related to Generalizations · 15
Kummer theory → AG, AG/π, Artin, Frobenius, G-module, Galois, H1, Hom, Kummer, Schreier, Suppose, Taking, Then, Witt, Witt's
related to For elliptic curves · 4
Kummer theory → E/K, Kummer, Let, There
related to Kummer map · 4
Kummer theory → Kummer, Let, Letting, One
is a · 2
Kummer theory → Kummer map, special case of this when A is the multiplicative group of the separable closure of a field k

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Important terminology

kummer field displaystyle theory group roots extensions extension unity galois nth characteristic map abelian cyclic also exponent case degree taking

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Kummer theoryis aKummer map0.90text
Kummer theoryis aspecial case of this when A is the multiplicative group of the separable closure of a field k0.90text
Kummer theoryrelated to For elliptic curvesKummer0.60section
Kummer theoryrelated to For elliptic curvesLet0.60section
Kummer theoryrelated to For elliptic curvesE/K0.60section
Kummer theoryrelated to For elliptic curvesThere0.60section
Kummer theoryrelated to GeneralizationsSuppose0.60section
Kummer theoryrelated to GeneralizationsG-module0.60section
Kummer theoryrelated to GeneralizationsH10.60section
Kummer theoryrelated to GeneralizationsThen0.60section
Kummer theoryrelated to GeneralizationsAG/π0.60section
Kummer theoryrelated to GeneralizationsAG0.60section

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