# fraction field

Given an integral domain^{} $R$, the fraction field of $R$ is the localization^{} ${S}^{-1}R$ of $R$ with respect to the multiplicative set $S=R\setminus \{0\}$. It is always a field.

Title | fraction field |
---|---|

Canonical name | FractionField |

Date of creation | 2013-03-22 11:50:27 |

Last modified on | 2013-03-22 11:50:27 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 8 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 13B30 |

Synonym | field of fractions |

Synonym | quotient field |

Related topic | Localization |

Related topic | RationalFunction |