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:
 * $\omega = e^{2 \pi i / 3} = \dfrac 1 2 \paren {i \sqrt 3 - 1}$

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

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

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

Also see

 * Eisenstein Integers form Subring of Complex Numbers