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Algebraic integer

In algebraic number theory, an algebraic integer is a complex number that is integral over the integers. That is, an algebraic integer is a complex root of some polynomial which is monic (its leading coefficient is 1) and has coefficients that are all integers. The set of all algebraic integers A is closed under addition, subtraction and multiplication…

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Finite generation of ring extension

Ring

Additional facts

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Map overview Semantic statistics

Algebraic integer

Nodes66
Edges65
Triples30
Avg. degree1.97
Density0.030303
Components1

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Algebraic integer

Top relations

related to Additional facts · 9
Algebraic integer → Abel, Any, Bézout, If, In, Ruffini, That, The, This
related to Examples · 7
Algebraic integer → If, In, It, Moreover, OK, See Quadratic, The
related to Ring · 4
Algebraic integer → In, The, This, Thus
is a · 3
Algebraic integer → complex number that is integral over the integers, complex root of some polynomial which is monic, integral element of a finite extension K / Q
related to Integral closure · 3
Algebraic integer → Again, Every, In
related to Definitions · 2
Algebraic integer → Let, The
related to Finite generation of ring extension · 2
Algebraic integer → For, The

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Important terminology

algebraic integer integers ring displaystyle mathbb polynomial monic number numbers field extension root coefficients generated integral also rational finitely complex

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Algebraic integeris acomplex number that is integral over the integers0.90text
Algebraic integeris acomplex root of some polynomial which is monic0.90text
Algebraic integeris aintegral element of a finite extension K / Q0.90text
Algebraic integerrelated to Additional factsAny0.60section
Algebraic integerrelated to Additional factsThis0.60section
Algebraic integerrelated to Additional factsAbel0.60section
Algebraic integerrelated to Additional factsRuffini0.60section
Algebraic integerrelated to Additional factsThe0.60section
Algebraic integerrelated to Additional factsBézout0.60section
Algebraic integerrelated to Additional factsIf0.60section
Algebraic integerrelated to Additional factsIn0.60section
Algebraic integerrelated to Additional factsThat0.60section

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