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gptkbp:instanceOf
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gptkb:mathematical_concept
algebraic integer
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gptkbp:closed
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addition
multiplication
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gptkbp:contains
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ordinary integers
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gptkbp:definedIn
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complex numbers of the form a + bω, where a, b are integers and ω is a primitive cube root of unity
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gptkbp:discriminant
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-3
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gptkbp:fieldOfFractions
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gptkb:Eisenstein_rational_numbers
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gptkbp:form
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hexagonal lattice
lattice in the complex plane
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gptkbp:hasIdealStructure
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principal ideal domain
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https://www.w3.org/2000/01/rdf-schema#label
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Eisenstein integers
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gptkbp:minimalPolynomialOfω
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x^2 + x + 1
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gptkbp:namedAfter
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gptkb:Gotthold_Eisenstein
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gptkbp:normFunction
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N(a + bω) = a^2 - ab + b^2
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gptkbp:primeFactorization
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unique up to units
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gptkbp:relatedTo
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Gaussian integers
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gptkbp:ringName
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Euclidean domain
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gptkbp:subringOf
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complex numbers
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gptkbp:symbol
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gptkb:ℤ[ω]
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gptkbp:unitElements
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1
-1
ω
-ω
-ω^2
ω^2
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gptkbp:usedIn
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algebraic number theory
number theory
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gptkbp:ω
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(-1 + √-3)/2
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gptkbp:bfsParent
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gptkb:Gotthold_Eisenstein
gptkb:Number_theory
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gptkbp:bfsLayer
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5
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