As most cohomological invariants, the cohomological dimension involves a choice of a "ring of coefficients" "R", with a prominent special case given by "R" = Z, the ring of integers. Let "G" be a discrete group, "R" a non-zero ring with a unit, and "RG" the group ring. The group "G" has cohomological dimension less than or equal to "n", denoted cd"R"("G") ≤ "n", if the trivial "RG"-module "R" has a projective resolution of length "n", i.e. there are projective "RG"-modules "P"0, ..., "P""n" and "RG"-module homomorphisms "d""k": "P""k"formula_1"P""k" − 1 ("k" = 1, ..., "n") and "d"0: "P"0formula_1"R", such that the image of "d""k" coincides with the kernel of "d""k" − 1 for "k" = 1, ..., "n" and the kernel of "d""n" is trivial.