Extension functors of generalized local cohomology modules

2018/10/24 by Alireza Vahidi, Vahidi, Alireza, Faisal Hassani +3
Mathematics · #13D07 #13D45 #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.1810.10217

openalex publication_date 2018/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a commutative Noetherian ring with non-zero identity, \mathfraka an ideal of R, M a finitely generated R--module, and X an arbitrary R--module. In this paper, for non-negative integers s, t and a finitely generated R--module N, we study the membership of Ext_R^s(N, H^t_\mathfraka(M, X)) in Serre subcategories of the category of R--modules and present some upper bounds for the injective dimension and the Bass numbers of H^t_\mathfraka(M, X). We also give some results on cofiniteness and minimaxness of H^t_\mathfraka(M, X) and finiteness of Ass_R(H^t_\mathfraka(M, X).

Related

• Extension functors of local cohomology modules
• Upper bounds for finiteness of generalized local cohomology modules
• Some results on generalized local cohomology modules
• Finiteness of extension functors of local cohomology modules
• Cofiniteness with respect to extension of Serre subcategories