Some results on the cofiniteness and annihilators of local cohomology modules

ABSTRACT

Let (R,𝔪) be a Noetherian local ring. In this paper, we give a new characterization for the universal catenaricity of R and the Cohen–Macaulayness of all its formal fibers, and we study the cofiniteness and annihilators of local cohomology modules.

KEYWORDS:

• Cofinite modules
• local cohomology
• universally catenary rings whose formal fibers are Cohen-Macaulay

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 13D45
• 14B15
• 13E05

Acknowledgments

The authors are deeply grateful to the referee for his/her careful reading of the paper and valuable suggestions.