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Generalized derivations in prime rings and Banach algebras

Asma AliBasudeb DharaShahoor Khan — 2014

Discussiones Mathematicae - General Algebra and Applications

Let R be a prime ring with extended centroid C, F a generalized derivation of R and n ≥ 1, m≥ 1 fixed integers. In this paper we study the situations: 1. ( F ( x y ) ) m = ( x y ) for all x,y ∈ I, where I is a nonzero ideal of R; 2. (F(x∘y))ⁿ=(x∘y)ⁿ for all x,y ∈ I, where I is a nonzero right ideal of R. Moreover, we also investigate the situation in semiprime rings and Banach algebras.

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