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