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Quadratic integer

In number theory, quadratic integers are a generalization of the usual integers to quadratic fields. A complex number is called a quadratic integer if it is a root of some monic polynomial (a polynomial whose leading coefficient is 1) of degree two whose coefficients are integers, i.e. quadratic integers are algebraic integers of degree two. Thus…

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Overview

History

Definition

Explicit representation

Norm and conjugation

Quadratic integer rings

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Map overview Semantic statistics

Quadratic integer

Nodes84
Edges83
Triples62
Avg. degree1.98
Density0.02381
Components1

How this topic connects Entity context

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Quadratic integer

Top relations

related to Examples of real quadratic integer rings · 16
Quadratic integer → Brahmagupta, Diophantine, DY, Euclidean, European, For, Indian, Its, Pell's, Penrose, Peter Gustav Lejeune Dirichlet, Pierre Fermat, Some, The, This, X2
related to Examples of complex quadratic integer rings · 7
Quadratic integer → Carl Gauss, Eisenstein, For, Gaussian, Kleinian, The, Therefore
related to Quadratic integer rings · 6
Quadratic integer → B2, Bx, Every, In, It, The
related to Units · 6
Quadratic integer → Eisenstein, For, Gaussian, If, In, It
related to Definition · 5
Quadratic integer → De2, Each, If, More, The
related to Euclidean rings of quadratic integers · 5
Quadratic integer → Db, Equipped, Euclidean, This, When
related to history · 5
Quadratic integer → Explicit, Medieval Indian, Pell's, Richard Dedekind, The
related to Principal rings of quadratic integers · 5
Quadratic integer → Dedekind, However, The, These, This
is a · 3
Quadratic integer → algebraic integer of degree two, square of its absolute value as a complex number, unit in the ring of the integers of Q
related to Explicit representation · 3
Quadratic integer → An, Here, This

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Important terminology

integers quadratic sqrt ring integer displaystyle number mathbb rings units complex principal textstyle algebraic norm real euclidean unique domain case

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Quadratic integeris aalgebraic integer of degree two0.90text
Quadratic integeris asquare of its absolute value as a complex number0.90text
Quadratic integeris aunit in the ring of the integers of Q0.90text
Quadratic integerrelated to DefinitionMore0.60section
Quadratic integerrelated to DefinitionEach0.60section
Quadratic integerrelated to DefinitionDe20.60section
Quadratic integerrelated to DefinitionIf0.60section
Quadratic integerrelated to DefinitionThe0.60section
Quadratic integerrelated to Euclidean rings of quadratic integersWhen0.60section
Quadratic integerrelated to Euclidean rings of quadratic integersEuclidean0.60section
Quadratic integerrelated to Euclidean rings of quadratic integersThis0.60section
Quadratic integerrelated to Euclidean rings of quadratic integersEquipped0.60section

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