Generalized Jordan derivations of Incidence Algebras

Abstract: For a given ring $\mathfrak{R}$ and a locally finite pre-ordered set $(X, \leq)$, consider $I(X, \mathfrak{R})$ to be the incidence algebra of $X$ over $\mathfrak{R}$. Motivated by a Xiao's result which states that every Jordan derivation of $I(X,\mathfrak{R})$ is a derivation in the case $\mathfrak{R}$ is $2$-torsion free, one proves that each generalized Jordan derivation of $I(X,\mathfrak{R})$ is a generalized derivation provided $\mathfrak{R}$ is $2$-torsion free, getting as a consequence the above mentioned result.