# prime radical

The prime radical or lower nilradical of a ring $R$ is the intersection of all the prime ideals^{} of $R$.

Note that the prime radical is the smallest semiprime ideal^{} of $R$, and that $R$ is a semiprime ring if and only if its prime radical is the zero ideal^{}.

Title | prime radical |
---|---|

Canonical name | PrimeRadical |

Date of creation | 2013-03-22 12:01:29 |

Last modified on | 2013-03-22 12:01:29 |

Owner | CWoo (3771) |

Last modified by | CWoo (3771) |

Numerical id | 7 |

Author | CWoo (3771) |

Entry type | Definition |

Classification | msc 16N80 |

Synonym | lower nilradical |

Related topic | RadicalOfAnIdeal |

Related topic | Nilradical |