CHARACTERIZATION OF MIXED TRIPLE DERIVATIONS ON INCIDENCE ALGEBRAS

Abstract

Let R be a 2-torsion free commutative unital ring and I(S, R) be the incidence algebra of a locally finite preordered set S. In the present paper, we show that if an R-linear map T : I(S, R) → I(S, R) satisfies T([t ◦ u, v]) = [T(t) ◦ u, v] + [t ◦ T(u), v] + [t ◦ u,T(v)], for all t, u, v ∈ I(S, R), then T = Ψ + ϕ, where Ψ : I(S, R) → I(S, R) is a derivation and ϕ : I(S, R) → Z(I(S, R)) is an R-linear map.