Nonlinear derivations of incidence algebras

Abstract

Let ( $$X,\leq$$ ) be a locally finite preordered set and R a 2-torsion free commutative ring with unity, I(X, R) the incidence algebra of X over R. We prove that each nonlinear derivation of I(X, R) is a sum of an inner derivation, a transitive induced derivation and an additive induced derivation. In particular, every nonlinear derivation of I(X, R) is automatically additive.