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Normal extension

In abstract algebra, a normal extension is an algebraic field extension L/K for which every irreducible polynomial over K that has a root in L splits into linear factors over L. This is one of the conditions for an algebraic extension to be a Galois extension. Bourbaki calls such an extension a quasi-Galois extension. For finite extensions, a normal…

Definition, Examples and counterexamples & Other properties

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Definition

Algebraic closureEmbeddingAutomorphism
3 related topics

Examples and counterexamples

Algebraic numbersPrimitive root of unity
2 related topics

Other properties

Compositum
1 related topics

Equivalent conditions for normality

Minimal polynomial
1 related topics

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Overview

Definition

Other properties

Equivalent conditions for normality

Examples and counterexamples

Normal closure

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Map overview Semantic statistics

Normal extension

Nodes23
Edges22
Triples27
Avg. degree1.91
Density0.086957
Components1

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Normal extension

Top relations

related to Examples and counterexamples · 9
Normal extension → For, Here, However, It, Let, On, Recall, The, Then
related to Equivalent conditions for normality · 6
Normal extension → All, Aut, L/K, Let, The, There
related to Definition · 4
Normal extension → Every, L/K, Let, Then
related to Other properties · 4
Normal extension → EF, If, Let, Then
related to Normal closure · 3
Normal extension → Furthermore, If, This
is a · 1
Normal extension → algebraic field extension L/K for which every irreducible polynomial over K that has a root in L splits into linear factors over L

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Important terminology

extension normal displaystyle field mathbb algebraic sqrt closure root conditions every polynomial splitting algebra overline irreducible splits one equivalent also

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Normal extensionis aalgebraic field extension L/K for which every irreducible polynomial over K that has a root in L splits into linear factors over L0.90text
Normal extensionrelated to DefinitionLet0.60section
Normal extensionrelated to DefinitionL/K0.60section
Normal extensionrelated to DefinitionThen0.60section
Normal extensionrelated to DefinitionEvery0.60section
Normal extensionrelated to Equivalent conditions for normalityLet0.60section
Normal extensionrelated to Equivalent conditions for normalityL/K0.60section
Normal extensionrelated to Equivalent conditions for normalityThe0.60section
Normal extensionrelated to Equivalent conditions for normalityThere0.60section
Normal extensionrelated to Equivalent conditions for normalityAll0.60section
Normal extensionrelated to Equivalent conditions for normalityAut0.60section
Normal extensionrelated to Examples and counterexamplesFor0.60section

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