Some Results on Partially Ordered Sets Involving Permuting n-derivations

The main objective of the present work, as a generalization of derivation, is to give the concept of permuting n-derivations on partially ordered sets (posets). Several associated theorems and fondamental properties involving permuting n-derivations are presented. Moreover, we demonstrate that if D is a permuting n-derivation on poset G with the greatest element 1 and the trace δ, then δ(1) = 1 if and only if δ is an identity on G. Furthermore, we discuss the relations among derivations, ideals and fixed sets in posets.