# zero module

Let $R$ be a ring.

The abelian group^{} which contains only an identity element^{} (zero)
gains a trivial $R$-module structure,
which we call the .

Every $R$-module $M$ has an zero element^{}
and thus a submodule^{} consisting of that element.
This is called the zero submodule of $M$.

Title | zero module |
---|---|

Canonical name | ZeroModule |

Date of creation | 2013-03-22 12:01:42 |

Last modified on | 2013-03-22 12:01:42 |

Owner | antizeus (11) |

Last modified by | antizeus (11) |

Numerical id | 6 |

Author | antizeus (11) |

Entry type | Definition |

Classification | msc 16D10 |

Synonym | zero submodule |

Related topic | ZeroIdeal |