On Symmetric Additive Mappings and Their Applications

The key motive of this paper is to study symmetric additive mappings and discuss their
applications. The study of these symmetric mappings makes it possible to characterize symmetric
n-derivations and describe the structure of the quotient ring S/P, where S is any ring and P is a
prime ideal of S. The symmetricity of additive mappings allows us to transfer ring theory results to
functional analyses, particularly to C�-algebras. Precisely, we describe the structures of C�-algebras
via symmetric additive mappings.