# integral closure

Let $B$ be a ring with a subring $A$. The integral closure^{} of $A$ in $B$ is the set ${A}^{\prime}\subset B$ consisting of all elements of $B$ which are integral over $A$.

It is a theorem that the integral closure of $A$ in $B$ is itself a ring. In the special case where $A=\mathbb{Z}$, the integral closure ${A}^{\prime}$ of $\mathbb{Z}$ is often called the ring of integers in $B$.

Title | integral closure |
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Canonical name | IntegralClosure |

Date of creation | 2013-03-22 12:07:53 |

Last modified on | 2013-03-22 12:07:53 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 8 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 13B22 |

Related topic | IntegrallyClosed |

Defines | ring of integers |