Abstract

This paper examines the orthogonality between reverse (𝛼,1)-derivation and symmetric reverse (𝛼,1)-biderivation in a 2 torsion-free semiprime ring. Several equivalences are established through lemmas and theorems that describe necessary and sufficient conditions for such mappings to be orthogonal. In particular, it is shown that orthogonality enforces bilinear identities in which special cases ensure that the associated mapping becomes a biderivation. These results extend previous studies on orthogonal derivations and biderivations while offering new perspectives on the structural properties of semiprime rings. This framework presented an open gap by characterizing the interaction of orthogonality between reverse (𝛼,1)-derivation and symmetric reverse (𝛼, 1)-biderivation. 

Keywords

Derivation, (𝛼,1)-derivation, reverse (𝛼,1)-derivation, reverse (α, 1)-biderivation, Semiprime Ring. 

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