Two-point differentiation for general orders

We establish a Zavadskij-type reduction for orders Λ in a finite-dimensional algebra over a complete field K with respect to a discrete valuation. For a suitable monomorphism u of Λ-lattices, we define a derived order δuΛ, and a functor ∂u between Λ- and δuΛ-lattices which yields an equivalence modulo finitely many indecomposables. The known versions of Zavadskijʹs differentiation algorithm (for tiled orders [15], representations of posets [14], and vector space categories [10,11]) are unified, and extended in this way to a part of representation theory of general orders.