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:
ACKNOWLEDGMENT
The authors are supported by Nafosted, Vietnam (Project No. 101.01.33.09).
Notes
Communicated by I. Swanson.