Eisenstein integer

== English == === Etymology === Named after Gotthold Eisenstein (1823–1852), German mathematician. === Noun === Eisenstein integer (plural Eisenstein integers) (algebra) A complex number of the form a + b ω {\displaystyle a+b\omega } , where a and b are integers and ω is defined by the following two rules: (1) ω 3 = 1 {\displaystyle \omega ^{3}=1} and (2) 1 + ω + ω 2 = 0 {\displaystyle 1+\omega +\omega ^{2}=0} ; an element of the Euclidean domain Z [ ω ] {\displaystyle \mathbb {Z} [\omega ]} . ==== Hypernyms ==== quadratic integer algebraic integer ==== Hyponyms ==== Eisenstein prime ==== See also ==== Gaussian integer