Generalized skew derivations on semiprime rings

Let be a semiprime ring with centre , its right Martindale quotient ring, its extended centroid, a generalized skew derivation of , associated with a non-zero skew derivation of , and fixed integers such that , for all . Then contains a non-zero central ideal. The case of centralizers (generalized skew derivations associated with a zero skew derivation) is also studied.