MMN-4167

# On traces of permuting n-derivations on prime ideals

*Hajar EL Mir*;

*Badr Nejjar*;

*Lahcen Oukhtite*;

## Abstract

In this article we investigate some properties of permuting n-derivations acting on a prime ideal.
More precisely, let $n \geq 2$ be a fixed positive integer, $P$ be a prime ideal of a ring $R$ such that $R/P$ is $(n+1)!$-torsion free. If there exists a permuting $n$-derivation $\Delta : R^{n} \longrightarrow R$ such that the trace $\delta$ of $\Delta$ satisfies $\overline{\big[[\delta (x),x],x\big]} \in Z(R/P)$ for all $x\in R$, then $\Delta(R^{n})\subseteq P$ or R/P is commutative.

Vol. 24 (2023), No. 3, pp. 1317-1327

DOI: 10.18514/MMN.2023.4167