LIE IDEALS WITH MULTIPLICATIVE (GENERALIZED)-DERIVATIONS OF SEMIPRIME RINGS
Abstract
Let R be a 2-torsion free semiprime ring, U a square-closed Lie ideal of R, f a multiplicative (generalized)-derivation with the additive map d of R: In the present
paper, we shall prove that R contains a nonzero central ideal if any one of the following
holds: i) F(x)F(y)±[x; y] ∈ Z, ii) F(x)F(y)±(x◦y) ∈ Z, iii) F([x; y]) = ±(xy ± yx), iv) F(x ◦ y) = ±(xy ± yx), v) F(xy) ± F(x)F(y) = 0, vi) F(xy) ± F(y)F(x) = 0 for all x; y ∈ U.
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DOI: https://doi.org/10.22190/FUMI240326026K
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