Geodesic
A Result on Prime Rings with Generalized Derivations
Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 2, pp. 439-446

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In this paper we investigate the following result. Let R be a prime ring, Q its symmetric Martindale quotient ring, C its extended centroid, I a nonzero ideal of R. If F and G are the two generalized derivation of R such that (F(xy) + G(yx))n − (xy ∓ yx)n = 0, for all x, y ∈ I, then either R is commutative or F (x) = x, G(x) = ∓x for all x ∈ R and n = 1.
Keywords: prime ring, generalized derivations, quotient ring, extended centroid 
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Shujat, Faiza; Khan, Shahoor. A Result on Prime Rings with Generalized Derivations. Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 2, pp. 439-446. http://geodesic.mathdoc.fr/item/DMGAA_2021_41_2_a14/