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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 <i>n</i>-derivations and describe the structure of the quotient ring <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="fraktur">S</mi><mo>/</mo><mi mathvariant="fraktur">P</mi></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">S</mi></semantics></math></inline-formula> is any ring and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">P</mi></semantics></math></inline-formula> is a prime ideal of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">S</mi></semantics></math></inline-formula>. The symmetricity of additive mappings allows us to transfer ring theory results to functional analyses, particularly to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mo>∗</mo></msup></semantics></math></inline-formula>-algebras. Precisely, we describe the structures of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mo>∗</mo></msup></semantics></math></inline-formula>-algebras via symmetric additive mappings.