# Goldie’s theorem

Let $R$ be a ring with an identity^{}. Then $R$ has a right classical ring of quotients $Q$ which is semisimple^{} Artinian^{} if and only if $R$ is a semiprime right Goldie ring. If this is the case, then the composition^{} length of $Q$ is equal to the uniform dimension of $R$.

An immediate corollary of this is that a semiprime right Noetherian ring always has a right classical ring of quotients.

This result was discovered by Alfred in the late 1950’s.

Title | Goldie’s theorem |
---|---|

Canonical name | GoldiesTheorem |

Date of creation | 2013-03-22 14:04:17 |

Last modified on | 2013-03-22 14:04:17 |

Owner | mclase (549) |

Last modified by | mclase (549) |

Numerical id | 7 |

Author | mclase (549) |

Entry type | Theorem |

Classification | msc 16U20 |

Classification | msc 16P60 |

Related topic | OresTheorem2 |