Additive derivations of incidence algebras

We study additive derivations of the incidence algebra I(X, R), where X is a preordered set and R is an algebra over some commutative ring. For a finite connected partially ordered set X, it is proved that the submodule of inner additive derivations is a direct summand of the module of all additive derivations of the algebra I(X, R). As a corollary of this main result of the paper, we found the structure of the module of inner additive derivations. We also obtain several criteria for matching of the submodule of inner additive derivations with the module of all additive derivations. Under the additional assumption that the center of the ring R is a field, the dimension of the space of additive derivations is calculated.