Nonlinear Jordan derivations of incidence algebras

Abstract

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