# semigroup

A semigroup^{} $G$ is a set together with a binary operation^{} $\cdot :G\times G\u27f6G$ which satisfies the associative property: $(a\cdot b)\cdot c=a\cdot (b\cdot c)$ for all $a,b,c\in G$.

The set $G$ is not required to be nonempty.

Let $G,H$ be two semigroups. A *semigroup homomorphism* from $G$ to $H$ is a function $f:G\to H$ such that $f(ab)=f(a)f(b)$.

Title | semigroup |

Canonical name | Semigroup |

Date of creation | 2013-03-22 11:50:08 |

Last modified on | 2013-03-22 11:50:08 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 11 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 20M99 |

Synonym | homomorphism^{} |

Related topic | groupoid^{} |

Related topic | Band2 |

Related topic | SubmonoidSubsemigroup |

Related topic | NullSemigroup |

Related topic | ZeroElements |

Related topic | Monoid |

Defines | semigroup homomorphism |