On the Catenaricity of Noetherian Local Rings and Quasi Unmixed Artinian Modules

Abstract

Let (R, 𝔪) be a Noetherian local ring, A an Artinian R-module, and M a finitely generated R-module. Consider the following property:

We say that A is quasi unmixed if for all In this article, we give a connection among the property (*) for a quasi unmixed Artinian module A, the catenaricity of the ring R/Ann _R A, and the dimension of A. Specially, we show that for an integer i ≥ 0, if the local cohomology module is quasi unmixed then satisfies the property (*) if and only if the ring is catenary and

Key Words:

• Catenaricity
• Quasi unmixed Artinian modules

2000 Mathematics Subject Classification:

• 13D45
• 13E05

ACKNOWLEDGMENT

The authors are supported by Nafosted, Vietnam (Project No. 101.01.33.09).

Notes

Communicated by I. Swanson.