# rig

A *rig* $(R,+,\cdot )$ is a set $R$ together with two binary operations^{} $+:{R}^{2}\to R:(a,b)\mapsto a+b$ and $\cdot :{R}^{2}\to R:(a,b)\mapsto ab$, such that both $(R,+)$ and $(R,\cdot )$ are monoids, where $\cdot $ distributes over $+$. That is if $\{a,b,c,d\}\subset R$ then $(a+b)(c+d)=ac+ad+bc+bd$. The natural numbers^{} with ordinary addition^{} and multiplication $(\mathbf{N},+,\cdot )$ is a rig.

A rig $(R,+,\cdot )$ is a ring if $(R,+)$ is a group. The integers with ordinary addition and multiplication $(\mathbf{Z},+,\cdot )$ is a ring.

Title | rig |
---|---|

Canonical name | Rig |

Date of creation | 2013-03-22 14:44:29 |

Last modified on | 2013-03-22 14:44:29 |

Owner | HkBst (6197) |

Last modified by | HkBst (6197) |

Numerical id | 8 |

Author | HkBst (6197) |

Entry type | Definition |

Classification | msc 20M99 |

Related topic | semigroup |

Related topic | ring |