Geodesic
Generalized derivations with left annihilator conditions in prime and semiprime rings
Discussiones Mathematicae. General Algebra and Applications, Tome 37 (2017) no. 2, pp. 161-175

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Let R be a prime ring with its Utumi ring of quotients U, C = Z(U) be the extended centroid of R, H and G two generalized derivations of R, L a noncentral Lie ideal of R, I a nonzero ideal of R. The left annihilator of S ⊆ R is denoted by lR(S) and defined by lR(S) = x ∈ R| xS = 0. Suppose that S = H(un)un +unG(un) | u ∈ L and T = H(xn)xn +xnG(xn) | x ∈ I, where n ≥ 1 is a fixed integer. In the paper, we investigate the cases when the sets lR(S) and lR(T) are nonzero.
Keywords: prime ring, derivation, Lie ideal, generalized derivation, Utumi quotient ring, extended centroid 
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     title = {Generalized derivations with left annihilator conditions in prime and semiprime rings},
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Dhara, Basudeb. Generalized derivations with left annihilator conditions in prime and semiprime rings. Discussiones Mathematicae. General Algebra and Applications, Tome 37 (2017) no. 2, pp. 161-175. http://geodesic.mathdoc.fr/item/DMGAA_2017_37_2_a4/