Orthogonal Symmetric Reverse Bi--Derivations in Semiprime Rings

Abstract

Suppose that and  are two symmetric reverse bi-(????, )-derivations of a semi prime ring R. In this paper, we establish some equivalent conditions for the orthogonality between two symmetric reverse bi-(????, )-derivations  , of  R. We prove that  and    are orthogonal if and only if any one of the following conditions is satisfied (i)  (ii)  (iii)     (iv)   is  a   bi- -derivation,  for all  .