Generalized derivations on Lie ideals in prime rings
Abstract
Let R be a prime ring with characteristic different from two, U a nonzero Lie ideal of R and f be a generalized derivation associated with d. We prove the following results: (i) If [u, f(u)] ∈ Z, for all u ∈ U, then U ⊂ Z. (ii) (f,d)and(g, h) be two generalized derivations of R such that f(u)v = ug(v), for all u, v ∈ U, then U ⊂ Z. (iii) f([u, v]) = ±[u, v], for all u, v ∈ U, then U ⊂ Z. Let R be a prime ring with characteristic different from two, U a nonzero Lie ideal of R and f be a generalized derivation associated with d. We prove the following results: (i) If [u, f(u)] ∈ Z, for all u ∈ U, then U ⊂ Z. (ii) (f,d)and(g, h) be two generalized derivations of R such that f(u)v = ug(v), for all u, v ∈ U, then U ⊂ Z. (iii) f([u, v]) = ±[u, v], for all u, v ∈ U, then U ⊂ Z.
Source
Turkish Journal of MathematicsVolume
35Issue
1URI
http://www.trdizin.gov.tr/publication/paper/detail/TVRFeE9UZ3pNdz09https://hdl.handle.net/20.500.12418/1907
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