2024/02/10 by Rafael Holanda, Holanda, Rafael, Cleto B. Miranda-Neto +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2402.06842
openalex publication_date 2024/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.