Orthogonality of left reverse derivation and symmetric left reverse biderivation in semiprime rings

This paper gives the notion of orthogonality between the left reverse derivation and symmetric left reverse biderivation of a semiprime ring. We prove that if R is a semiprime ring, B is a reverse biderivation and d is a derivation of R are orthogonal if and only if any one of the following equivalent conditions hold for every x,y,z∈R. (i)B(x,y)d(z)+d(x)B(z,y)=0 (ii) dB=0 (iii) d(x)B(x,y)=0 (iv) dB is a biderivation.