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.
Facts
Finite or Infinite Eisenstein Integers
Filter Results1 entry
Connections
Attributed To
Source Eisenstein integer (Wikipedia)
In Branch
Source Eisenstein integer (Wikipedia)
Is Kind Of Object
Principal Result Of
Source Eisenstein Integers (Wikipedia)
Sources
1. Eisenstein Integer, from Wolfram MathWorld
Page textQuote, Page text
Eisenstein integers are complex numbers that are members of the imaginary quadratic field, which is precisely the ring (Wagon 1991, p.
2. Eisenstein integer (Wikipedia)
Eisenstein Integers (Wikipedia)
Principal Result Of: Gotthold Eisenstein, Lead sentence of the article on the resultQuote, Principal Result Of: Gotthold Eisenstein, Lead sentence of the article on the result
In mathematics, the Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are the complex numbers of the form z = a + b ω , {\displaystyle z=a+b\omega ,} where a and b are integers and ω = − 1 + i 3 2 = e i 2 π / 3 {\displaystyle \omega ={\frac {-1+i{\sqrt {3}}}{2}}=e^{i2\pi /3}} is a primitive (hence non-real) cube root of unity.
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.