Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
mathematical ring
|
| gptkbp:alsoKnownAs |
ring of Eisenstein integers
|
| gptkbp:basisOverℤ |
{1, ω}
|
| gptkbp:contains |
all Eisenstein integers
|
| gptkbp:definedIn |
set of numbers of the form a + bω, where a, b ∈ ℤ and ω is a primitive cube root of unity
|
| gptkbp:dimensionOverℤ |
2
|
| gptkbp:discriminant |
-3
|
| gptkbp:fieldOfFractions |
ℚ(ω)
|
| gptkbp:hasSubgroup |
complex numbers
|
| gptkbp:hasUnit |
±1, ±ω, ±ω^2
|
| https://www.w3.org/2000/01/rdf-schema#label |
ℤ[ω]
|
| gptkbp:isEuclideanDomain |
true
|
| gptkbp:isIntegralDomain |
true
|
| gptkbp:isPrincipalIdealDomain |
true
|
| gptkbp:isUniqueFactorizationDomain |
true
|
| gptkbp:norm |
N(a + bω) = a^2 - ab + b^2
|
| gptkbp:usedIn |
gptkb:geometry_of_numbers
algebraic number theory cryptography modular forms |
| gptkbp:ω |
(-1 + √-3)/2
|
| gptkbp:bfsParent |
gptkb:Eisenstein_integer
gptkb:Eisenstein_integers |
| gptkbp:bfsLayer |
6
|