A Generalization of Formal Local Cohomology Modules

Let a and Ii be two ideals of a commutative Noetherian ring R, M a finitely generated R-module and i an integer. In this paper we study formal local cohomology modules with respect to a pair of ideals. We denote the i-th a-formal local cohomology module M with respect to b by (sic)(i)(a,b)(M). We show that if (sic)(i)(a,b)(M) is artinian, then a subset of root(0: (sic)(i)(a,b)(M)). Also, we show that (sic)(dim)(M)(a,b) (M) is artinian and we determine the set Att(R) (sic)(dim)(M)(a,b)(M).