\begin{definition}[Definition:Ring of Eisenstein Integers]
The '''ring of Eisenstein integers''' $\struct {\Z \sqbrk \omega, +, \times}$ is the algebraic structure formed from:
:the set of Eisenstein integers $\Z \sqbrk \omega$, where $\omega = e^{2 \pi i / 3}$
:the operation of complex addition
:the operation of complex multiplication.
\end{definition}