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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:application
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gptkb:Algebraic_geometry
gptkb:Class_field_theory
Cryptography
Solving Diophantine equations
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gptkbp:baseField
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Rational numbers
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gptkbp:contains
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Algebraic numbers
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gptkbp:defines
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Finite degree field extension of the rational numbers Q
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gptkbp:example
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Q(cube_root(2))
Q(i)
Q(sqrt(2))
Q(zeta_n)
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gptkbp:fieldOfStudy
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gptkb:Algebraic_number_theory
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gptkbp:generalizes
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gptkb:Cyclotomic_fields
gptkb:Quadratic_fields
Rational numbers
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gptkbp:hasInvariant
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gptkb:Weyl_group
Degree
Class number
Discriminant
Unit group
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gptkbp:hasProperty
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Every element is algebraic over Q
Finite dimension as a vector space over Q
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gptkbp:hasSubfield
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gptkb:Kummer_extension
Galois extension
Cubic field
Cyclotomic field
Quadratic field
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https://www.w3.org/2000/01/rdf-schema#label
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Algebraic Number Fields
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gptkbp:isA
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Number field
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gptkbp:notablePerson
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gptkb:Carl_Friedrich_Gauss
gptkb:David_Hilbert
gptkb:Emil_Artin
gptkb:Kurt_Hensel
gptkb:Leopold_Kronecker
gptkb:Richard_Dedekind
gptkb:Ernst_Kummer
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gptkbp:relatedTo
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gptkb:Dedekind_domain
gptkb:Minkowski's_theorem
gptkb:Dirichlet's_unit_theorem
gptkb:Hilbert_class_field
gptkb:Kronecker–Weber_theorem
gptkb:Artin_reciprocity
gptkb:Zeta_function_of_a_number_field
L-functions
Prime ideals
Algebraic integers
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gptkbp:structure
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Ring of integers
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gptkbp:studiedBy
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Mathematicians
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gptkbp:studiedIn
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19th century
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gptkbp:bfsParent
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gptkb:Igor_Shafarevich
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gptkbp:bfsLayer
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6
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