Systems of Parameters and the Cohen-Macaulay Property

2014/12/18 by Katharine Shultis, Shultis, Katharine · 1 citation
Mathematics · #13C05 #13H10 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13C05 #msc:13H10

paper · pdf · doi:10.48550/arxiv.1412.5912

arxiv created 2014/12/18 · arxiv updated 2014/12/19

Abstract

Let R be a commutative, Noetherian, local ring and M an R-module. Consider the module of homomorphisms Hom_R(R/\mathfraka,M/\mathfrakb M) where \mathfrakb⊆\mathfraka are parameter ideals of M. When M=R and R is Cohen-Macaulay, Rees showed that this module of homomorphisms is always isomorphic to R/\mathfraka, and in particular, a free module over R/\mathfraka of rank one. In this work, we study the structure of such modules of homomorphisms for general M.

Cited by

• Comparing the face rings of a boolean complex and its barycentric subdivision

Related

• Local Homology and Local Cohomology
• Reducing system of parameters and the Cohen--Macaulay property
• Modules of reduction number one
• Relative Cohen-Macaulay modules under ring homomorphisms
• Local Homology, Cohen-Macaulayness and Cohen-Macaulayfications