Nonlinear Jordan derivations of incidence algebras

Let (X, <=) be a locally finite preordered set, R a two-torsion-free commutative ring with unity and I(X, R)the incidence algebra of X over R: In this paper, all the nonlinear Jordan derivations of I(X, R)are determined. In particular, if all the connected components of X are nontrivial, we prove that every nonlinear Jordan derivation of I(X, R)is proper and can be presented as a sum of an inner derivation, a transitive induced derivation, and an additive induced derivation.