Attached primes of local cohomology modules with respect to a pair of ideals

The paper shows an extension of the Lichtenbaum-Hartshorne Vanishing theorem for local cohomology modules with respect to a pair of ideals. We also study the attached primes of top local cohomology module H-I,J(c) (M), where c = sup{i | H-I,J(i) (M) not equal 0}. In the case, where c = dimM - 1, we show that Att(R)(H-I, J(dimM-1) (M)) boolean AND V (J) = {p is an element of Supp(R) M boolean AND V (J) | cd(I, R/ p) = dimM - 1}.