On functional identities involving n-derivations in rings

Abstract

In this paper, we explore various properties associated with the traces of permuting $n$-derivations satisfying certain functional identities that operate on a Lie ideal within prime and semiprime rings. Additionally, we address and discusscorrelated findings pertaining to left $n$-multipliers. Lastly, we enrich our results with examples that show the necessity of their assumptions.

Keywords

• semiprime ring
• lie ideal
• derivation
• symmetric $n$-derivation
• $n$-multiplier