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

This paper is concerned with the relation between localcohomology modules defined by a pair of ideals and serre classes ofr-modules. let r be a commutative noetherian ring, i , j be twoideals of r and m be an r-module. let a 2 ?w (i, j) and t 2 n0be such that exttr(r/a,m) 2 s and extjr(r/a,hii,j (m)) 2 s for alli < t and all j > 0. then for any submodule n of hti,j (m) such thatext1r(r/a,n) 2 s, we obtain homr(r/a,hti,j (m)/n) 2 s.