Bulletin of the
Korean Mathematical Society BKMS

Let $R$ be a $3$-torsion free semiprime ring and let $I$ be a nonzero two-sided ideal of $R$. Suppose that there exists a permuting 3-derivation $\D : R\times R\times R \to R$ such that the trace is centralizing on $I$. Then the trace of $\D$ is commuting on $I$. In particular, if $R$ is a $3!$-torsion free prime ring and $\D$ is nonzero under the same condition, then $R$ is commutative.

Keywords: prime ring, semiprime ring, commuting map, centralizing map, derivation, bi-derivation, 3-derivation

MSC numbers: 16W20, 16W25