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 
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/
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