# Eisenstein integers

Let $\rho =(-1+\sqrt{-3})/2$, where we arbitrarily choose $\sqrt{-3}$ to be either of the complex numbers^{} whose square is $-3$. Note that ${\rho}^{3}=1$. The *Eisenstein integers ^{}* are the ring $\mathbb{Z}[\rho ]=\{a+b\rho :a,b\in \mathbb{Z}\}$.

Title | Eisenstein integers |

Canonical name | EisensteinIntegers |

Date of creation | 2013-03-22 11:45:35 |

Last modified on | 2013-03-22 11:45:35 |

Owner | KimJ (5) |

Last modified by | KimJ (5) |

Numerical id | 13 |

Author | KimJ (5) |

Entry type | Definition |

Classification | msc 11R04 |

Classification | msc 65A05 |

Classification | msc 65D20 |

Classification | msc 00-01 |

Classification | msc 11Y70 |

Classification | msc 18-00 |

Related topic | GaussianIntegers |

Related topic | ComplexNumber |

Related topic | NumberField |

Related topic | EisenteinPrime |