Geodesic
Left Annihilator of Identities with Generalized Derivations in Prime and Semiprime Rings
Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 1, pp. 69-79

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Let R be a noncommutative prime ring of char (R) ≠ 2, F a generalized derivation of R associated to the derivation d of R and I a nonzero ideal of R. Let S ⊆ R. The left annihilator of S in R is denoted by lR(S) and defined by lR (S) = x ∈ R | xS = 0. In the present paper, we study the left annihilator of the sets F(x) ◦n F(y)−x ◦n y | x, y ∈ I and F(x) ◦n F(y)−d(x ◦n y) | x, y ∈ I.
Keywords: prime ring, derivation, generalized derivation, extended centroid, Utumi quotient ring 
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Rahaman, Md Hamidur. Left Annihilator of Identities with Generalized Derivations in Prime and Semiprime Rings. Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 1, pp. 69-79. http://geodesic.mathdoc.fr/item/DMGAA_2021_41_1_a6/