Abstract
Let R be a prime ring of characteristic different from 2 with center Z and extended centroid C, and let L be a Lie ideal of R. Consider two nontrivial automorphisms α and β of R for which there exist integers m,n ≥ 1 such that α(u)n + β(u)m = 0 for all u ∈ L. It is shown that, under these assumptions, either L is central or R ⊆ M2(C) (where M2(C) is the ring of 2 × 2 matrices over C), L is commutative, and u2 ∈ Z for all u ∈ L. In particular, if L =[R, R], then R is commutative.
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Russian Text © The Author(s), 2020, published in Matematicheskie Zametki, 2020, Vol. 107, No. 1, pp. 106–111.
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Rehman, N. On Lie Ideals and Automorphisms in Prime Rings. Math Notes 107, 140–144 (2020). https://doi.org/10.1134/S0001434620010137
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DOI: https://doi.org/10.1134/S0001434620010137