Jordan derivations of incidence algebras

Abstract

Let $\mathcal{R}$ be a commutative ring with identity and $I(X,\mathcal{R})$ the incidence algebra of a locally finite pre-ordered set $X$. In this note, we characterize the derivations of $I(X,\mathcal{R})$ and prove that every Jordan derivation of $I(X,\mathcal{R})$ is a derivation, provided that $\mathcal{R}$ is $2$-torsion free.