TOP LOCAL COHOMOLOGY MODULES WITH RESPECT TO A PAIR OF IDEALS

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(I,J)(dimM)(M). We get some results about attached prime ideals of the local cohomology module As a consequence, we find that there exists a quotient L of M such that H(I,J)(dimM)(M) congruent to H(I)(dimM)(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.