Some Results on Graded Generalized Local Cohomology Modules

Abstract

. Let R = ⊕n>0Rn be a graded Noetherian ring with local base ring R0 and let R+ = ⊕n>1Rn. Let M and N be finitely generated graded R-modules. In this paper we extend some of the known results about ordinary local cohomology modules Hi R+ (M) to generalized local cohomology modules Hi R+ (M, N). Indeed, among other things, we prove that certain submodules and factor modules of Hi R+ (M, N) are Artinian for some i. Also we obtain some results on the asymptotic behaviour of the n-th graded components Hi R+ (M, N)n of Hi R+ (M, N) for n −→ −∞