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gptkbp:instanceOf
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algebraic integer
complex number
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gptkbp:closed
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addition
multiplication
subtraction
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gptkbp:definedIn
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complex number of the form a + bω where a, b are integers and ω is a primitive cube root of unity
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gptkbp:form
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hexagonal lattice in the complex plane
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gptkbp:generalizes
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gptkb:Gaussian_integer
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gptkbp:hasNorm
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N(a + bω) = a^2 - ab + b^2
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gptkbp:hasUniqueFactorization
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true
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gptkbp:hasUnit
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±1, ±ω, ±ω^2
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https://www.w3.org/2000/01/rdf-schema#label
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Eisenstein integer
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gptkbp:isCommutativeRing
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true
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gptkbp:isCountable
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true
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gptkbp:isDedekindDomain
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true
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gptkbp:isDiscreteSubgroupOf
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complex numbers under addition
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gptkbp:isEuclideanDomain
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true
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gptkbp:isFinite
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true
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gptkbp:isIntegralDomain
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true
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gptkbp:isNoetherianRing
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true
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gptkbp:isPrincipalIdealDomain
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true
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gptkbp:isSubringOf
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complex numbers
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gptkbp:namedAfter
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gptkb:Ferdinand_Eisenstein
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gptkbp:primitiveCubeRootOfUnity
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ω = (-1 + sqrt(-3))/2
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gptkbp:ringOfIntegersOf
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Q(ω)
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gptkbp:symbol
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gptkb:ℤ[ω]
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gptkbp:usedIn
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algebraic number theory
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gptkbp:bfsParent
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gptkb:Ferdinand_Eisenstein
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gptkbp:bfsLayer
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5
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