We construct the cochain N‐complex by means of an associative unital graded algebra and prove that the generalized cohomologies of this cochain N‐complex are trivial. We also show that this cochain N‐complex can be endowed with the strucure of graded q‐differential algebra. We apply this construction to generalized Clifford algebra which allows us to construct an analog of differential forms with exterior differential satisfying dN = 0 on a reduced quantum plane. We introduce the algebra of polynomials and endow it with the structure of graded q‐differential algebra.