Local Cohomology Modules and Relative Cohen-Macaulayness

Abstract

Let (R, 𝔪) denote a commutative Noetherian local ring and let M be a finite R-module. In this paper, we study relative Cohen-Macaulay rings with respect to a proper ideal 𝔞 of R and give some results on such rings in relation with Artinianness, Non-Artinianness of local cohomology modules and Lyubeznik numbers. We also present some related examples to this issue.

Keywords

• local cohomology modules
• lyubeznik numbers
• non-artinian modules
• relative cohen-macaulayness
• primary 13d45
• secondary 13c14, 13e10