Category:Definitions/Eisenstein Integers

This category contains definitions related to Eisenstein Integers.
Related results can be found in Category:Eisenstein Integers.

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 $\Z \sqbrk \omega$:

$\Z \sqbrk \omega = \set {a + b \omega: a, b \in \Z}$