2022/05/31 by Xiaolei Zhang, Hwankoo Kım, Zhang, Xiaolei +3
Mathematics · Medicine · #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Intracranial Aneurysms: Treatment and Complications #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2205.15583
openalex publication_date 2022/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Parkash and Kour obtained a new version of Cohen's theorem for Noetherian modules, which states that a finitely generated R-module M is Noetherian if and only if for every prime ideal \mathfrakp of R with Ann(M)⊆ \mathfrakp, there exists a finitely generated submodule N^\mathfrakp of M such that \mathfrakp M⊆ N^\mathfrakp⊆ M(\mathfrakp), where M(\mathfrakp)=\x∈ M| sx∈ \mathfrakp M for some s∈ R ∖ \mathfrakp \. In this paper, we generalize the Parkash and Kour version of Cohen's theorem for Noetherian modules to those for S-Noetherian modules and w-Noetherian modules.