# Eisenstein integers

Let $\rho=(-1+\sqrt{-3})/2$, where we arbitrarily choose $\sqrt{-3}$ to be either of the complex numbers whose square is $-3$. Note that ${\rho}^{3}=1$. The Eisenstein integers are the ring $\mathbb{Z}[\rho]=\{a+b\rho:a,b\in\mathbb{Z}\}$.

 Title Eisenstein integers Canonical name EisensteinIntegers Date of creation 2013-03-22 11:45:35 Last modified on 2013-03-22 11:45:35 Owner KimJ (5) Last modified by KimJ (5) Numerical id 13 Author KimJ (5) Entry type Definition Classification msc 11R04 Classification msc 65A05 Classification msc 65D20 Classification msc 00-01 Classification msc 11Y70 Classification msc 18-00 Related topic GaussianIntegers Related topic ComplexNumber Related topic NumberField Related topic EisenteinPrime