Modules whose finiteness dimensions coincide with their cohomological dimensions

2020/01/08 by Divaani-Aazar, Kamran, Doust, Akram Ghanbari, Tousi, Massoud +1
#13C05 #13C14 #13D45 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2001.02470

Abstract

Let a be an ideal of a commutative Noetherian ring R with identity. We study finitely generated R-modules M whose a-finiteness and a-cohomological dimensions are equal. In particular, we examine relative analogues of quasi-Buchsbaum, Buchsbaum and surjective Buchsbaum modules. We reveal several interactions between these types of modules that extend some of the existing results in the classical theory to the relative one.

Related

• The finiteness dimension of modules and relative Cohen-Macaulayness
• Finiteness dimensions and cofiniteness of generalized local cohomology modules
• The finiteness dimension of local cohomology modules and its dual notion
• Cohomological dimension and relative Cohen-Maculayness
• Modules cofinite with respect to ideals of small dimensions