Central Values of X-generalized Skew Derivations on Right Ideals in Prime Rings

Abstract

AbstractLet R be a prime ring of characteristic different from 2, Q its right Martindale quotient ring, C its extended centroid, I a right ideal of R, \(a\in Q\), G a nonzero X-generalized skew derivation of R, \(f(x_1,\ldots ,x_n)\) a multilinear polynomial over C with n non-commuting variables, and S the set of the evaluations of \(f(x_1,\ldots ,x_n)\) on I. If \([f(x_1,\ldots ,x_n),x_{n+1}]x_{n+2}\) is not an identity for I and \(aG(x)x\in Z(R)\) for all \(x\in S\), then we determine all the possible forms of G.KeywordsGeneralized skew derivationMultilinear polynomialPrime ring