Orthogonal Generalized Symmetric Reverse Bi-(\(\sigma,\tau\))-Derivations of Semi Prime Ring

Abstract

Let R be a semi prime ring. Suppose that \(\sigma,\pi\)  are automorphisms on R.  A symmetric bi-additive mapping \(\delta1:RXR\to R\)  is said to be a generalized symmetric reverse Bi-(\(\sigma,\pi\))-derivation on R if there exists a symmetric reverse Bi-(\(\sigma,\pi\))-derivation D on R such that holds . Let   ] and ] be two generalized symmetric reverse Bi-(\(\sigma,\pi\))-derivations of R  with associated  reverse  bi- -derivations . In this paper, we establish some equivalent conditions for the orthogonality between two symmetric generalized reverse Bi-(\(\sigma,\pi\))-derivations of semiprime ring R.