Abstract
Let R be a prime ring with characteristic different from 2, let U be a nonzero Lie ideal of R, and let f be a generalized derivation associated with d. We prove the following results: (i) If a ∈ R and [a, f(U)] = 0 then a ∈ Z or d(a) = 0 or U ⊂ Z; (ii) If f 2(U) = 0 then U ⊂ Z; (iii) If u 2 ∈ U for all u ∈ U and f acts as a homomorphism or antihomomorphism on U then either d = 0 or U ⊂ Z.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 47, No. 5, pp. 1052–1057, September–October, 2006.
Original Russian Text Copyright © 2006 Gölbaşi Ö. and Kaya K.
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Gölbaşi, Ö., Kaya, K. On Lie ideals with generalized derivations. Sib Math J 47, 862–866 (2006). https://doi.org/10.1007/s11202-006-0094-6
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DOI: https://doi.org/10.1007/s11202-006-0094-6