Some Results on Graded Generalized Local Cohomology Modules

Let R = circle minus(n) >= R-0(n) be a graded Noetherian ring with local base ring R-0 and let R+ = circle minus(n) >= R-1(n). 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 H-R(i) (+)(M) to generalized local cohomology modules H-R +(i)(M, N). Indeed, among other things, we prove that certain submodules and factor modules of H-R +(i)(M, N) are Artinian for some i. Also we obtain some results on the asymptotic behaviour of the n-th graded components H-R +(i)(M, N) n of H-R +(i)(M, N) for n -> - infinity.