# commutative semigroup

A semigroup^{} $S$ is *commutative ^{}* if the defining binary operation

^{}is commutative (http://planetmath.org/Commutative). That is, for all $x,y\in S$, the identity

^{}$xy=yx$ holds.

Although the term *Abelian semigroup* is sometimes used, it is more common simply to refer to such semigroups as *commutative semigroups*.

A monoid which is also a commutative semigroup is called a *commutative monoid*.

Title | commutative semigroup |
---|---|

Canonical name | CommutativeSemigroup |

Date of creation | 2013-03-22 13:08:09 |

Last modified on | 2013-03-22 13:08:09 |

Owner | mclase (549) |

Last modified by | mclase (549) |

Numerical id | 4 |

Author | mclase (549) |

Entry type | Definition |

Classification | msc 20M14 |

Synonym | Abelian semigroup |

Related topic | AbelianGroup |

Related topic | AbelianGroup2 |

Defines | commutative |

Defines | commutative monoid |