The Eisenstein integers, named after Gotthold Eisenstein and occasionally called Eulerian integers after Leonhard Euler, are the complex numbers of the form a plus b times omega, where a and b are ordinary integers and omega is a primitive, non-real cube root of unity. They form a triangular lattice in the complex plane, in contrast to the Gaussian integers, which form a square lattice, and like the Gaussian integers they make up a countably infinite set.
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Sources
1. Eisenstein Integer, from Wolfram MathWorld
Definition, first paragraphQuote, Definition, first paragraph
Eisenstein integers are complex numbers that are members of the imaginary quadratic field Q(√-3), which is precisely the ring Z[ω]
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