Local-Global Principle for the Artinianness of Local Cohomology Modules

Abstract

Let R be a commutative Noetherian ring, I a proper ideal of R, and M a finitely generated R-module. We prove that there is a local-global principle for the Artinianness of the local cohomology module , i.e., for any integer n > 0, is Artinian for all i < n if and only if is Artinian for all i < n and all prime ideals 𝔭, which deduces one interesting property of filter depth.

Key Words:

• Artinianness
• Local cohomology module
• Local-global principle

2000 Mathematics Subject Classification:

• 13D45
• 13E10
• 14B15

ACKNOWLEDGMENT

Supported by the National Natural Science Foundation of China and the Natural Science Foundation of Jiangsu Province.

Notes

Communicated by A. Singh.