Definition:Ring of Eisenstein Integers

Definition

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.

Also see

• Eisenstein Integers form Subring of Complex Numbers