Year: 2024
Type: preprint
Abstract: The main purpose of this note is to extend and establish a new approach to the concept of (relative) Cohen-Macaulayness, by investigating the cohomological dimension as well as the depth of a pair of modules over a commutative Noetherian ring. The notion also largely extends the cohomologically complete intersection property of Hellus and Schenzel. As crucial tools, we use Herzog's theory of generalized local cohomology along with spectral sequence techniques. We also provide byproducts concerning two classical problems in homological commutative algebra.
Source: arXiv (Cornell University)
Authors: Holanda, Rafael, Miranda-Neto, Cleto B.
Institution: Universidade Federal da Paraíba
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G3633094627, G5918322612, G8302394166
OpenAlex ID: W4391800547