Abstract
In the present paper we prove that, let R be a prime ring with center Z, L a Lie ideal of R and \(\sigma \) a nontrivial automorphism of R such that (i)\(\{ \sigma (u)\}^n -(u)^{2m+1} =0\), (ii)\(\{ \sigma (u)\}^n -(u)^{2m+1} \in Z\), (iii) \(\{ \sigma (u)\}^n +(u)^{2m} =0\) \(\text{ for } \text{ all }~~u\in L\) and fixed \(n,m \ge 1\). If either char \((R)> n+1\) or char \((R) = 0\), then \(L\subseteq Z\).
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Bano, T., Ur Rehman, N. Some identities on automorphisms in prime rings. Rend. Circ. Mat. Palermo, II. Ser 66, 375–381 (2017). https://doi.org/10.1007/s12215-016-0260-z
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DOI: https://doi.org/10.1007/s12215-016-0260-z