# modular law

Let ${}_{R}M$ be a left $R$-module with submodules $A,B,C$, and suppose $C\subseteq B$. Then

$$C+(B\cap A)=B\cap (C+A)$$ |

This result shows that the submodules of ${}_{R}M$, partially ordered by inclusion, form a modular lattice^{} with $\cap $ as the meet and $+$ as the join (http://planetmath.org/Join).

Title | modular law |
---|---|

Canonical name | ModularLaw |

Date of creation | 2013-03-22 12:50:42 |

Last modified on | 2013-03-22 12:50:42 |

Owner | yark (2760) |

Last modified by | yark (2760) |

Numerical id | 7 |

Author | yark (2760) |

Entry type | Theorem |

Classification | msc 16D10 |

Related topic | ModularLattice |