Some Results on Graded Generalized Local Cohomology Modules

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.