GENERALIZED FORMAL LOCAL COHOMOLOGY MODULES

Let a be an ideal of a local ring (R,m) and M and N two finitely generated R-modules. In this paper, we introduce the concept of generalized formal local cohomology modules. We define i-th generalized formal local cohomology module of M and N with respect to a by Fi a(M,N) := l←im− n Hi m(M,N/anN) for i ≥ 0. We prove several results concerning vanishing and finiteness properties of these modules