Tag Archives: Orthogonal Derivation

Orthogonal Symmetric Bi Derivations in Semiprime Rings (Published)

In this paper we introduce the notation of orthogonal symmetric bi derivations in semiprime ring and we consider R be a 2-torsion free semiprime ring, B and D are two symmetric bi derivations on R,then B and D are orthogonal if and only if one of the following equivalent conditions holds for all x,y,z∈R: (1) BD=0. (2) B(x,y)D(y,z)=0 or D(x,y)B(y,z)=0.(3) BD is a bi derivation. (4) B(x,y)D(y,z)+D(y,z)B(x,y)=0,for every x,y,z ∈R.

Keywords: Bi Derivation, Derivation, Jordan Bi Derivation., Orthogonal Derivation, Orthogonal Symmetric Bi Derivation, Semi Prime Ring