Ulrich module

A maximal Cohen-Macaulay module M over a NoetherianPlanetmathPlanetmathPlanetmath local ringMathworldPlanetmath (R,𝔪,k) is Ulrich if e(M)=μ(M), where e(M) is the Hilbert-Samuel multiplicity of M and μ(M) is the minimal number of generatorsPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath of M. When M is a maximal Cohen-Macaulay module and 𝔪 has a minimal reduction I generated by a system of parameters, M is Ulrich if and only if 𝔪M=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