On Cohen's theorem for Artinian modules

2022/05/31 by Xiaolei Zhang, Hwankoo Kım, Zhang, Xiaolei +3
Mathematics · #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2205.15586

openalex publication_date 2022/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that a finitely embedded R-module M is Artinian if and only if for every prime ideal \mathfrakp of R with (0:_RM)⊆ \mathfrakp, there exists a submodule N^\mathfrakp of M such that M/N^\mathfrakp is finitely embedded and M[\mathfrakp]⊆ N^\mathfrakp⊆ (0:_M\mathfrakp).

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