Some results on the cohomological dimension of two modules on a pair of ideals

‎Let $R$ be a commutative Noetherian ring‎, ‎$I,~J$ be two ideals of $R$‎, ‎and $M,~N$ be‎ ‎two $R$-modules‎. ‎We introduce the cohomological dimension of $N‎, ‎M$ with respect to $(I,J)$‎, ‎as‎ ‎${m cd}(I‎, ‎J‎, ‎N‎, ‎M)=sup{iin Bbb N_0‎: ‎H_{I,J}^{i}(N‎, ‎M)eq0}$‎, and we investigate some properties of this invariant‎‎‎‎‎‎‎‎‎‎‎‎. ‎