Abstract
The aim of the paper is to study the commuting generalized derivations. Suppose that R is a prime ring of char\((R)\ne 2\), \(\pi (\xi _1,\ldots ,\xi _n)\) is a noncentral multilinear polynomial over C and \(T_1\), \(T_2\) and \(T_3\) are generalized derivations on R. If \(T_2(\xi )T_1(\xi )=T_1(\xi )\xi -\xi T_3(\xi )\) for all \(\xi =\pi (\xi _1,\ldots ,\xi _n)\in f(R)\), then we describe all possible forms of \(T_1\), \(T_2\) and \(T_3\).
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The authors are grateful to the referee for carefully reading the manuscript. The valuable suggestions have simplified and clarified the paper greatly. The author also thanks to Prof. Daniel Levcovitz, ICMC-USP for his suggestions.
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This work is supported by the PNPD-CAPES Fellowship under the direction of Prof. Daniel Levcovitz.
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Tiwari, S.K. Product and commuting generalized derivations in prime rings. Rend. Circ. Mat. Palermo, II. Ser 72, 1377–1397 (2023). https://doi.org/10.1007/s12215-022-00739-6
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DOI: https://doi.org/10.1007/s12215-022-00739-6