# module of finite rank

Let $M$ be a module,
and let $E(M)$ be the injective hull of $M$.
Then we say that $M$ has
if $E(M)$ is a finite direct sum^{}
of indecomposable^{} submodules.

This turns out to be equivalent^{} to the property
that $M$ has no infinite^{} direct sums of nonzero submodules.

Title | module of finite rank |
---|---|

Canonical name | ModuleOfFiniteRank |

Date of creation | 2013-03-22 12:03:24 |

Last modified on | 2013-03-22 12:03:24 |

Owner | antizeus (11) |

Last modified by | antizeus (11) |

Numerical id | 8 |

Author | antizeus (11) |

Entry type | Definition |

Classification | msc 16D80 |