# prime ring

A ring $R$ is said to be a *prime ring ^{}* if the zero ideal

^{}is a prime ideal

^{}.

If a prime ring $R$ is commutative^{}, then it is a cancellation ring. If in $R$ has a multiplicative identity^{} $1\ne 0$, then it is an integral domain^{}.

Title | prime ring |
---|---|

Canonical name | PrimeRing |

Date of creation | 2013-03-22 11:51:05 |

Last modified on | 2013-03-22 11:51:05 |

Owner | Wkbj79 (1863) |

Last modified by | Wkbj79 (1863) |

Numerical id | 10 |

Author | Wkbj79 (1863) |

Entry type | Definition |

Classification | msc 16U99 |

Classification | msc 16N60 |

Related topic | ZeroIdeal |