Nonlinear Jordan derivations of finitary incidence algebras

Abstract

Let P be a partially ordered set, a 2-torsion free commutative ring with unity and the finitary incidence algebra of P over . In this paper, we give an explicit description for the structure of nonlinear Jordan derivations of . We show that if P has no trivial component, then every nonlinear Jordan derivation of is proper, and can be presented as a sum of a generalized inner derivation, a transitive induced derivation and an additive induced derivation. If P has a trivial connected component, we prove that every nonlinear Jordan derivation of is proper if and only if every nonlinear Jordan derivation of R is also proper.