\begin{definition}[Definition:Eisenstein Prime]
Let $\Z \sqbrk \omega$ be the ring of Eisenstein integers.
Let $\alpha \in \Z \sqbrk \omega$ be an Eisenstein integer.
Then $\alpha$ is an '''Eisenstein prime''' {{iff}} $\alpha$ is prime in $\Z \sqbrk \omega$.
{{NamedforDef|Ferdinand Gotthold Max Eisenstein|cat = Eisenstein}}
Category:Definitions/Number Theory
Category:Definitions/Eisenstein Integers
Category:Definitions/Prime Elements of Rings
\end{definition}