cofiniteness of generalized local cohomology modules

Let r be a commutative noetherian ring with non-zero identity and i be an ideal of r. let m and n be two finitely generated r-modules such that pd_r(m) < ∞. in this paper we establish some results concerning the cofiniteness of generalized local cohomology modules. specifically, we show that if q(i,r) ≤ 1, then h^i_i (m,n) is i-cofinite for each i ≥ 0. as aconsequence, it follows that ext^i_r(l,h^j_i(m,n)) and tor^r_i(l,h^j_i (m,n)) are i-cofinite for each i ≥ 0 and j ≥ 0. finally, we show that, if cd_i (m,r) = 2 and h_i^2(m,r) is i-cofinite, then h^i_i (m,n) is i-cofinite for each i ≥ 0