UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES

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 hi a(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 hi a(m;n) belongs to s for all i > n.