Action of $ n $-derivations and $ n $-multipliers on ideals of (semi)-prime rings.

The present paper aims to investigate the containment of nonzero central ideal in a ring R when the trace of symmetric n -derivations satisfies some differential identities. Lastly, we prove that in a prime ring R of suitable torsion restriction, if D , G : R n → R are two nonzero symmetric n -derivations such that f (ϑ) ϑ + ϑ g (ϑ) = 0 holds ∀ ϑ ∈ W , a nonzero left ideal of R where f and g are the traces of D and G , respectively, then either R is commutative or G acts as a left n -multiplier. Finally, we characterize symmetric n -derivations in terms of left n -multipliers. [ABSTRACT FROM AUTHOR]