Abstract
Let U be the Utumi quotient ring of a prime ring R, char\((R)\ne 2\) and \(f(x_1,\ldots ,x_n)\) be a noncentral multilinear polynomial over the extended centroid C. Suppose that G, F and H are three generalized derivations on R such that \(F(G(f(r))f(r))-H(f(r)^2)=0\) for all \(r=(r_1,\ldots ,r_n)\in R^{n}\). In this paper, we give the complete characterization of the mappings G, F and H.
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Tiwari, S.K. Identities with generalized derivations in prime rings. Rend. Circ. Mat. Palermo, II. Ser 71, 207–223 (2022). https://doi.org/10.1007/s12215-021-00627-5
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DOI: https://doi.org/10.1007/s12215-021-00627-5