Abstract
Let be a noncommutative prime ring of characteristic different from 2, be the right Martindale quotient ring of and be the extended centroid of . Suppose that is a noncentral multilinear polynomial over and are three generalized skew-derivations of associated to the same automorphism α. Let be the associated skew derivations respectively of and such that h, f, g are commuting with α. We will provide the complete description of and , in the case for all .
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