# semi-local ring

A ring $R$ is *semi-local* if $R/rad(R)$ is an Artinian ring, where $rad(R)$ denotes the Jacobson radical^{} of $R$. In the case that $R$ is commutative^{}, this reduces to the definition that $R$ is *semi-local* if $R$ has finitely many maximal ideals^{}. Note that finite rings are trivially semi-local.

Title | semi-local ring |
---|---|

Canonical name | SemilocalRing |

Date of creation | 2013-03-22 12:56:42 |

Last modified on | 2013-03-22 12:56:42 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 7 |

Author | mathcam (2727) |

Entry type | Definition |

Classification | msc 16L30 |

Classification | msc 13H99 |

Synonym | semilocal ring |

Related topic | LocalRing |