GENERALIZED LOCAL COHOMOLOGY AND SERRE COHOMOLOGICAL DIMENSION.

Let R be a commutative Noetherian ring, I, J be two ideals of R, and M, N be two R-modules. Let S be a Serre subcategory of the category of R-modules. We introduce Serre cohomological dimension of N, M with respect to (I, J), as cdS(I, J, N, M) = sup{i ∈ N₀ : Hⁱ_I,J (N, M) 6∈ S}. We study some properties of cdS(I, J, N, M), and we get some formulas and upper bounds for it. [ABSTRACT FROM AUTHOR]