# Ulrich module

A maximal Cohen-Macaulay module $M$ over a Noetherian^{} local ring^{} $(R,\U0001d52a,k)$ is Ulrich if $e(M)=\mu (M)$, where $e(M)$ is the Hilbert-Samuel multiplicity of $M$ and $\mu (M)$ is the minimal number of generators^{} of $M$. When $M$ is a maximal Cohen-Macaulay module and $\U0001d52a$ has a minimal reduction $I$ generated by a system of parameters, $M$ is Ulrich if and only if $\U0001d52aM=IM$.

Title | Ulrich module |
---|---|

Canonical name | UlrichModule |

Date of creation | 2013-03-22 18:13:38 |

Last modified on | 2013-03-22 18:13:38 |

Owner | yshen (21076) |

Last modified by | yshen (21076) |

Numerical id | 8 |

Author | yshen (21076) |

Entry type | Definition |

Classification | msc 13C14 |