# natural homomorphism

The *natural homomorphism ^{}* $R\to R/I$ where $R$ is a ring and $I$ an ideal of $R$ is the map $\alpha \mapsto \alpha +I$. Coset operations

^{}, e.g $(\alpha +\beta )+I=(\alpha +I)+(\beta +I)$ guarantee this will be a homomorphism

^{}. Natural homomorphisms for groups can be defined similarly.

Title | natural homomorphism |
---|---|

Canonical name | NaturalHomomorphism |

Date of creation | 2013-03-22 14:33:32 |

Last modified on | 2013-03-22 14:33:32 |

Owner | iwnbap (1760) |

Last modified by | iwnbap (1760) |

Numerical id | 8 |

Author | iwnbap (1760) |

Entry type | Definition |

Classification | msc 13B10 |

Related topic | Homomorphism |

Related topic | QuotientRing |

Defines | Natural homomorphism |