Document Type : Original Manuscript


Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395- 4697, 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 $i\geq 0$. We prove several results concerning vanishing and finiteness properties of these modules.


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