# prime element

An element $p$ in a ring $R$ is a prime element^{} if it generates a prime ideal^{}. If $R$ is commutative, this is equivalent^{} to saying that for all $a,b\in R$ , if $p$ divides $ab$, then $p$ divides $a$ or $p$ divides $b$.

When $R=\mathbb{Z}$ the prime elements as formulated above are simply prime numbers.

Title | prime element |
---|---|

Canonical name | PrimeElement |

Date of creation | 2013-03-22 12:46:52 |

Last modified on | 2013-03-22 12:46:52 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 7 |

Author | drini (3) |

Entry type | Definition |

Classification | msc 13C99 |

Classification | msc 16D99 |

Synonym | prime |

Related topic | PrimeIdeal |

Related topic | DivisibilityInRings |

Related topic | DivisibilityByPrimeNumber |