# algebraic integer

Let $K$ be an extension^{} (http://planetmath.org/ExtensionField) of $\mathbb{Q}$ contained in $\u2102$. A number $\alpha \in K$ is called an *algebraic integer ^{}* of $K$ if it is the root of a monic polynomial with coefficients in $\mathbb{Z}$, i.e., an element of $K$ that is integral over $\mathbb{Z}$. Every algebraic integer is an algebraic number

^{}(with $K=\u2102$), but the converse

^{}is false.

Title | algebraic integer |

Canonical name | AlgebraicInteger |

Date of creation | 2013-03-22 11:45:41 |

Last modified on | 2013-03-22 11:45:41 |

Owner | KimJ (5) |

Last modified by | KimJ (5) |

Numerical id | 13 |

Author | KimJ (5) |

Entry type | Definition |

Classification | msc 11R04 |

Classification | msc 62-01 |

Classification | msc 03-01 |

Related topic | IntegralBasis |

Related topic | CyclotomicUnitsAreAlgebraicUnits |

Related topic | FundamentalUnits |

Related topic | Monic2 |

Related topic | RingWithoutIrreducibles |