On ideals preserving generalized local cohomology modules

Let R be a commutative Noetherian ring, a an ideal of R and M, N two finitely generated R-modules. Let t be a positive integer or infinity. We denote by Omega(t) the set of ideals c such that H-c(i) ( M, N) congruent to H-a(i) (M, N) for all i < t. First, we show that there exists the ideal b(t) which is the largest in Omega(t) and dim R/b(t) = sup(i<t) dim Supp H-a(i) (M, N). Next, we prove that if partial derivative is an ideal such that a subset of partial derivative subset of b(t), then H-partial derivative(i) ( M, N) congruent to H-a(i) ( M, N) for all i < t.