Shahram Rezaei - Department of Mathematics, Payame Noor University (PNU), P.O. Box ۱۹۳۹۵- ۴۶۹۷, Tehran, Iran.
Fatemeh Lashkari - Department of Mathematics, Payame Noor University (PNU), P.O. Box ۱۹۳۹۵- ۴۶۹۷, Tehran, Iran.

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  \mathfrak{F}_{a}^i(M,N) := \underset{n}{\varprojlim}H_m^i(M,N/{a}^{n}N ) for i\geq ۰. We prove several results concerning vanishing and finiteness properties of these modules.

formal local cohomology, Local cohomology, Generalized