ON TRACES OF PERMUTING n-DERIVATIONS ON PRIME IDEALS

In this article we investigate some properties of permuting n-derivations acting on a prime ideal. More precisely, let n >= 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 -> R such that the trace delta of Delta satisfies ([[delta(x),x],x]) over bar is an element of Z(R/P) for all x is an element of R, then Delta(R-n) subset of P or R/P is commutative.