UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCALCOHOMOLOGY MODULES

Let R be a commutative Noetherian ring with non-zero identity and a an ideal of R. Let M be a nite R{module of nite projective dimension and N an arbitrary nite 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 de ne 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. Then, for any ideal b ? a, it is also shown that the module Hna (M;N)=bHna (M;N) belongs to S.

Keywords:

Generalized local cohomology module , Serre subcategory , Cohomological dimension