On generalization of two results of Foxby

2026/07/18 by Tony J. Puthenpurakal
#math.AC

paper · pdf

Abstract

Let (A,\mathfrakm) be a Noetherian local ring of dimension d and let M be a finitely generated A-module. Assume M has rank r > 0. We show that if M is NOT Cohen-Macaulay then μ_d(\mathfrakm, M) > r. If further A is unmixed and μ_n(\mathfrakm, M) ≤ 1 for some n ≥ d then we prove injdim M < ∞ and A is Cohen-Macaulay.

Related

• On the existence of certain modules of finite Gorenstein homological dimensions
• A criterion of Cohen Macaulayness of the form module
• On the structure of finitely generated modules and the unmixed degrees
• Local Homology, Cohen-Macaulayness and Cohen-Macaulayfications
• Criteria for finite injective dimension of modules over a local ring