Finiteness of extension functors of generalized local cohomology modules

Abstract

Let R be a commutative Noetherian ring with non-zero identity, a 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 s R (N, H t a (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 a (M, X). We also give some results on cofiniteness and minimaxness of H t a (M, X) and finiteness of Ass R (H t a (M, X)).