# principal ideal

Let $R$ be a ring and let $a\in R$. The principal left (resp. right, 2-sided) ideal of $a$ is the smallest left (resp. right, 2-sided) ideal of $R$ containing the element $a$.

When $R$ is a commutative ring, the principal ideal^{} of $a$ is denoted $(a)$.

Title | principal ideal |
---|---|

Canonical name | PrincipalIdeal |

Date of creation | 2013-03-22 11:51:49 |

Last modified on | 2013-03-22 11:51:49 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 7 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 13A15 |

Classification | msc 16D25 |

Classification | msc 81-00 |

Classification | msc 82-00 |

Classification | msc 83-00 |

Classification | msc 46L05 |