2011/08/02 by Moharram Aghapournahr, Aghapournahr, Moharram
Mathematics · #13D45 #14B15 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1108.0549
openalex publication_date 2011/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R be a commutative Noetherian ring with non-zero identity and \fa an ideal of R. Let M be a finite R--module of of finite projective dimension and N an arbitrary finite R--module. We characterize the membership of the generalized local cohomology modules \lci\fa(M,N) in certain Serre subcategories of the category of modules from upper bounds. We define and study the properties of a generalization of cohomological dimension of generalized local cohomology modules. Let \mathcal S be a Serre subcategory of the category of R--modules and n \geqslant \pd M be an integer such that \lci\fa(M,N) belongs to \mathcal S for all i> n. If \fb is an ideal of R such that \lcn\fa(M,N/\fbN) belongs to \mathcal S, It is also shown that the module \lcn\fa(M,N)/\fb\lcn\fa(M,N) belongs to \mathcal S.