Nonlinear Lie derivations of incidence algebras of finite rank.

Let (X , ≤) be a finite preordered set, R a 2-torsion free commutative ring with unity and I (X , R) the incidence algebra of X over R. In this paper we prove that every nonlinear Lie derivation of I (X , R) is of the standard form. More explicitly, each nonlinear Lie derivation of I (X , R) is a sum of an inner derivation, a transitive induced derivation, an additive induced derivation and a central-valued map. [ABSTRACT FROM AUTHOR]