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gptkbp:instanceOf
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algebraic number field
number field
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gptkbp:contains
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n-th roots of unity
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gptkbp:definedIn
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field extension of the rationals generated by a primitive n-th root of unity
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gptkbp:degree_over_Q
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φ(n)
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gptkbp:discriminant
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given by a formula involving n and its prime divisors
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gptkbp:example
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gptkb:Q(ζ_5)
Q(ζ_3) is Q(√-3)
Q(ζ_4) is Q(i)
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gptkbp:Galois_group
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isomorphic to (Z/nZ)×
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https://www.w3.org/2000/01/rdf-schema#label
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cyclotomic field
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gptkbp:minimal_polynomial_of_generator
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gptkb:cyclotomic_polynomial
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gptkbp:notation
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gptkb:Q(ζ_n)
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gptkbp:ramified_primes
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primes dividing n
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gptkbp:relatedTo
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abelian extensions of Q
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gptkbp:ring_of_integers
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gptkb:cyclotomic_integers
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gptkbp:splitting_field_of
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x^n - 1 over Q
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gptkbp:studiedBy
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gptkb:Weber
gptkb:Gauss
gptkb:Kronecker
gptkb:Kummer
algebraic number theory
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gptkbp:unramified_outside
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primes dividing n
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gptkbp:used_in
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gptkb:Fermat's_Last_Theorem
gptkb:Kronecker–Weber_theorem
class field theory
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gptkbp:bfsParent
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gptkb:Kronecker-Weber_theorem
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gptkbp:bfsLayer
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5
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