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 HiR
+(M) to generalized local
cohomology modules HiR
+(M,N). Indeed, among other things, we
prove that certain submodules and factor modules of HiR
+(M,N) are
Artinian for some i. Also we obtain some results on the asymptotic
behaviour of the n-th graded components HiR
+(M,N)n of HiR
+(M,N)
for n −! −1.