The finiteness dimension of modules and relative Cohen-Macaulayness

2017/02/01 by Zohouri, M. Mast, Amoli, Kh. Ahmadi
#13D45 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1702.00175

Abstract

Let R be a commutative Noetherian ring, \mathfrak a and \mathfrak b ideals of R. In this paper, we study the finiteness dimension f_{\mathfrak a}(M) of M relative to \mathfrak a and the \mathfrak b-minimum \mathfrak a-adjusted depth λ_{\mathfrak a}^{\mathfrak b}(M) of M, where the underlying module M is relative Cohen-Macaulay w.r.t \mathfrak a. Some applications of such modules are given.

Related

• Modules whose finiteness dimensions coincide with their cohomological dimensions
• The finiteness dimension of local cohomology modules and its dual notion
• Homological dimensions, the Gorenstein property, and special cases of some conjectures
• Cohomological dimension and relative Cohen-Maculayness
• Finiteness dimensions and cofiniteness of generalized local cohomology modules