On Functional Identities Involving -Derivations in Semiprime Rings

Abstract

This paper investigates -additive maps, known as symmetric -derivations whose trace satisfies certain algebraic identities. We establish various results that enhance our understanding of these maps, notably their occurrence in semiprime rings and the behavior of rings under particular algebraic identities involving nonzero ideal. Furthermore, we prove that the semiprime ring possesses a nonzero central ideal under certain algebraic conditions.