Definition:Eisenstein Integer

Definition
An Eisenstein integer is a complex number of the form
 * $a + b \omega$

where $a$ and $b$ are both integers and:
 * $\omega = e^{2 \pi i / 3} = \dfrac 1 2 \left({i \sqrt 3 - 1}\right)$

that is, the (complex) cube roots of unity.

The set of all Eisenstein integers can be denoted $\Z \left[{\omega}\right]$:
 * $\Z \left[{\omega}\right] = \left\{{a + b \omega: a, b \in \Z}\right\}$

Also known as
The Eisenstein integers are also known as the Eulerian integers.

Also see

 * Ring of Eisenstein Integers