Local Homology, Cohen-Macaulayness and Cohen-Macaulayfications

2005/07/07 by Michael Hellus, Hellus, Michael · 1 citation
Mathematics · #13C14 #13D45 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #msc:13C14 #msc:13D45

paper · pdf · doi:10.48550/arxiv.math/0507137

5 pages

arxiv created 2005/07/07 · openalex publication_date 2005/07/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (R,m) be a local, complete ring, X an artinian R-module of Noetherian dimension d; let x₁,...,x_d∈ m be such that 0:_X (x₁,...,x_d)R has finite length. Then H^x_d(X) is a finite R-module, providing a positive answer to a question posed by Tang. As a first application of this result corollory 1 contains a necessary condition for a finite module to be CM; secondly we propose a notion of Cohen-Macaulayfication and prove its uniqueness (th. 3); finally we show that this new notion of Cohen-Macaulayfication is a direct generalization of a notion of Cohen-Macaulayfication introduced by Goto (th. 4).

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