Eisenstein integer

Etymology
Named after (1823–1852), German mathematician.

Noun

 * 1)  A complex number of the form $$a + b \omega$$, where a and b are integers and &omega; is defined by the following two rules: (1) $$\omega^3 = 1$$ and (2) $$ 1 + \omega + \omega^2 = 0$$; an element of the Euclidean domain $$\mathbb{Z}[\omega]$$.
 * To divide an Eisenstein integer $$a + b\omega$$ by another Eisenstein integer $$c + d\omega$$, notice that $$(c + d\omega) (c + d) (c + d\omega^2) = c^3 + d^3$$; accordingly multiply both denominator and numerator (of the division expressed as a fraction) by $$(c + d)(c + d\omega^2)$$, then simplify.

Hypernyms

 * algebraic integer
 * algebraic integer