On the Local Cohomology Modules Defined by a Pair of Ideals and Serre Subcategory

This paper is concerned with the relation between local cohomology modules defined by a pair of ideals and Serre classes of R-modules. Let R be a commutative Noetherian ring, I , J be two ideals of R and M be an R-module. Let a 2 ?W (I, J) and t 2 N0 be such that Extt R(R/a,M) 2 S and Extj R(R/a,Hi I,J (M)) 2 S for all i < t and all j > 0. Then for any submodule N of Ht I,J (M) such that Ext1 R(R/a,N) 2 S, we obtain HomR(R/a,Ht I,J (M)/N) 2 S.