# null semigroup

A *left zero semigroup* is a semigroup in which every element is a left zero element. In other words, it is a set $S$ with a product defined as $xy=x$ for all $x,y\in S$.

A *right zero semigroup* is defined similarly.

Let $S$ be a semigroup. Then $S$ is a *null semigroup* if it has a zero element and if the product of any two elements is zero. In other words, there is an element $\theta \in S$ such that $xy=\theta $ for all $x,y\in S$.

Title | null semigroup |
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Canonical name | NullSemigroup |

Date of creation | 2013-03-22 13:02:22 |

Last modified on | 2013-03-22 13:02:22 |

Owner | mclase (549) |

Last modified by | mclase (549) |

Numerical id | 4 |

Author | mclase (549) |

Entry type | Definition |

Classification | msc 20M99 |

Related topic | Semigroup |

Related topic | ZeroElements |

Defines | null semigroup |

Defines | left zero semigroup |

Defines | right zero semigroup |