Let , where we arbitrarily choose to be either of the complex numbers whose square is . Note that . The Eisenstein integers are the ring .
![$ \mathbb{Z}[ \rho ] = \{ a + b \rho : a , b \in \mathbb{Z} \}$](http://images.planetmath.org:8080/cache/objects/208/l2h/img5.png "$ \mathbb{Z}[ \rho ] = \{ a + b \rho : a , b \in \mathbb{Z} \}$"){kind=small}