# total ring of fractions

For a commutative ring $R$ having regular elements^{}, we may form $T={S}^{-1}R$, the total ring of fractions^{} (quotients) of $R$, as the localization^{} of $R$ at $S$, where $S$ is the set of all non-zero-divisors of $R$. Then, $T$ can be regarded as an extension ring of $R$ (similarly as the field of fractions^{} of an integral domain^{} is an extension ring). $T$ has the non-zero unity 1.

Title | total ring of fractions |
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Canonical name | TotalRingOfFractions |

Date of creation | 2013-03-22 14:22:31 |

Last modified on | 2013-03-22 14:22:31 |

Owner | pahio (2872) |

Last modified by | pahio (2872) |

Numerical id | 13 |

Author | pahio (2872) |

Entry type | Definition |

Classification | msc 13B30 |

Synonym | total ring of quotients |

Related topic | ExtensionByLocalization |

Related topic | FractionField |