Abstract
Let R be a prime ring of characteristic different from 2, Q r be its right Martindale quotient ring and C be its extended centroid. Suppose that F, G are generalized skew derivations of R and \({f(x_1, \ldots, x_n)}\) is a non-central multilinear polynomial over C with n non-commuting variables. If F and G satisfy the following condition:
for all \({r_1, \ldots, r_n \in R}\), then we describe all possible forms of F and G.
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This work was partially supported by the Training Program of International Exchange and Cooperation of the Beijing Institute of Technology. The work of the third author was partially supported by the National Natural Science Foundation of China (Grant No. 10871023).
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Carini, L., De Filippis, V. & Wei, F. Generalized Skew Derivations Cocentralizing Multilinear Polynomials. Mediterr. J. Math. 13, 2397–2424 (2016). https://doi.org/10.1007/s00009-015-0631-2
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DOI: https://doi.org/10.1007/s00009-015-0631-2