Abstract
Let R be a prime ring of characteristic not equal to 2, Z(R) its center, Qr its right Martindale quotient ring, C its extended centroid, f ( x 1 , … , x n ) a non-central multilinear polynomial over C and u , v ∈ Q r . Suppose that F and H are two b-generalized skew derivations of R with associated terms ( b , α , d ) and ( b , α , δ ) . In this article we study the complete structure of F and H satisfying uF ( f ( X ) ) f ( X ) + F ( f ( X ) ) f ( X ) v = H ( f ( X ) 2 ) for any X = ( r 1 , … , r n ) ∈ R n .
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