# integrally closed

A subring $R$ of a commutative ring $S$ is said to be integrally closed^{} in $S$ if whenever $\theta \in S$ and $\theta $ is integral over $R$, then $\theta \in R$.

The integral closure^{} of $R$ in $S$ is integrally closed in $S$.

An integral domain^{} $R$ is said to be integrally closed (or ) if it is integrally closed in its fraction field.

Title | integrally closed |
---|---|

Canonical name | IntegrallyClosed |

Date of creation | 2013-03-22 12:36:34 |

Last modified on | 2013-03-22 12:36:34 |

Owner | rmilson (146) |

Last modified by | rmilson (146) |

Numerical id | 15 |

Author | rmilson (146) |

Entry type | Definition |

Classification | msc 13B22 |

Classification | msc 11R04 |

Synonym | normal ring |

Related topic | IntegralClosure |

Related topic | AlgebraicClosure |

Related topic | AlgebraicallyClosed |