Permuting Tri-Derivations on Posets

Let P be a partially ordered set (poset). The main objective of the present paper is to introduce and study the idea of permuting tri-derivations of posets. Several characterization theorems involving permuting tri-derivations are given. In particular, we prove that if d1 and d2 are two permuting tri-derivations of P with traces ϕ1 and ϕ2, then ϕ1 ≤ ϕ2 if and only if ϕ2(ϕ1(x)) = ϕ1(x) for all x ∈ P.