Top local cohomology modules with respect to a pair of ideals

Abstract

Let (R, m) be a commutative Noetherian local ring, and let I and J be two proper ideals of R. Let M be a non-zero finitely generated R-module. We investigate the top local cohomology module H dim M I, J (M). We get some results about attached prime ideals of the local cohomology module H dim M I, J (M). As a consequence, we find that there exists a quotient L of M such that H dim M I, J (M) ≅ H dim M I (L). Also, we give the generalized version of the Lichtenbaum-Hartshorne Vanishing Theorem for local cohomology modules of a finitely generated module with respect to a pair of ideals.