SOME RESULTS ON TOP LOCAL COHOMOLOGY MODULES WITH RESPECT TO A PAIR OF IDEALS

Let I and J be ideals of a Noetherian local ring (R, m) and let M be a nonzero finitely generated R-module. We study the relation between the vanishing of H-I,J(dimM) (M) and the comparison of certain ideal topologies. Also, we characterize when the integral closure of an ideal relative to the Noetherian R-module M/JM is equal to its integral closure relative to the Artinian R-module H-I,J(dimM) (M).