Nonlinear Jordan derivations of finitary incidence algebras.

Let P be a partially ordered set, R a 2-torsion free commutative ring with unity and F I (P , R) the finitary incidence algebra of P over R. In this paper, we give an explicit description for the structure of nonlinear Jordan derivations of F I (P , R) . We show that if P has no trivial component, then every nonlinear Jordan derivation of F I (P , R) 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 F I (P , R) is proper if and only if every nonlinear Jordan derivation of R is also proper. [ABSTRACT FROM AUTHOR]