# faithful module

Let $R$ be a ring, and let $M$ be an $R$-module.
We say that $M$ is a faithful $R$-module
if its annihilator^{} ${\mathrm{ann}}_{R}(M)$ is the zero ideal^{}.

We say that $M$ is a fully faithful $R$-module if every nonzero $R$-submodule of $M$ is faithful.

Title | faithful module |
---|---|

Canonical name | FaithfulModule |

Date of creation | 2013-03-22 12:01:35 |

Last modified on | 2013-03-22 12:01:35 |

Owner | antizeus (11) |

Last modified by | antizeus (11) |

Numerical id | 7 |

Author | antizeus (11) |

Entry type | Definition |

Classification | msc 16D80 |

Synonym | fully faithful module |