# Rees factor

Let $I$ be an ideal of a semigroup^{} $S$. Define a congruence^{} $\sim $ by $x\sim y$ iff $x=y$ or $x,y\in I$.

Then the *Rees factor* of $S$ by $I$ is the quotient $S/\sim $. As a matter of notation, the congruence $\sim $ is normally suppressed, and the quotient is simply written $S/I$.

Note that a Rees factor always has a zero element. Intuitively, the quotient identifies all element in $I$ and the resulting element is a zero element.

Title | Rees factor |
---|---|

Canonical name | ReesFactor |

Date of creation | 2013-03-22 13:05:46 |

Last modified on | 2013-03-22 13:05:46 |

Owner | mclase (549) |

Last modified by | mclase (549) |

Numerical id | 4 |

Author | mclase (549) |

Entry type | Definition |

Classification | msc 20M12 |

Classification | msc 20M10 |

Related topic | Ideal3 |