UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES

Document Type : Original Manuscript

Author

Department of Mathematics, Faculty of Science, Arak University, Arak, 38156-8-8349, Iran.

Abstract

Let R be a commutative Noetherian ring with non-zero identity and a an ideal of R. Let M be a finite R--module
of finite projective dimension and N an arbitrary finite R--module. We characterize the membership of the generalized local cohomology modules Hai(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 S be a Serre subcategory of the category of R--modules and n>pdM be an integer such that Hai(M,N) belongs to S for all i>n. Then, for any ideal b⊇a, it is also shown that the module Han(M,N)/bHan(M,N) belongs to S.

Keywords

Journal of Algebraic Systems
Volume 1, Issue 1 - Serial Number 1
September 2013
Pages 1-9

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