Abstract
Let R be a prime ring with center Z ( R ) , right Martindale quotient ring Q and extended centroid C . By a b -generalized derivation we mean an additive mapping g : R → Q such that g ( x y ) = g ( x ) y + b x d ( y ) for all x , y ∈ R , where b ∈ Q and d : R → Q is an additive map. In this paper, we extend some well-known results concerning (generalized) derivations on prime rings to b -generalized derivations. Further we investigate b -generalized derivation acting as a homomorphism or anti-homomorphism in a prime ring.
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