Symmetric Reverse n-Derivations on Ideals of Semiprime Rings

This paper focuses on examining a new type of n-additive maps called the symmetric reverse n-derivations. As implied by its name, it combines the ideas of n-additive maps and reverse derivations, with a $1$-reverse derivation being the ordinary reverse derivation. We explore several findings that expand our knowledge of these maps, particularly their presence in semiprime rings and the way rings respond to specific functional identities involving elements of ideals. Also, we provide examples to help clarify the concept of symmetric reverse n-derivations. This study aims to deepen the understanding of these symmetric maps and their properties within mathematical structures.