Communications of the
Korean Mathematical Society CKMS

In this paper, we introduce the notion of permuting $n$-deri\-vations in near-ring $N$ and investigate commutativity of addition and multiplication of $N$. Further, under certain constrants on a $n!$-torsion free prime near-ring $N$, it is shown that a permuting $n$-additive mapping $D$ on $N$ is zero if the trace $d$ of $D$ is zero. Finally, some more related results are also obtained.

Keywords: left near-rings, zero symmetric, derivations, permuting $n$-derivations