Generalized derivations in prime rings and Banach algebras
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2014, Vol 34, Issue 1
Abstract
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) n 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. Keywords: prime ring, generalized derivation, extended centroid, Utumi quotient ring. 2010 Mathematics Subject Classification: 16N60, 16U80, 16W25.
Authors and Affiliations
Shahoor Khan, Asma Ali, Basudeb Dhara
Keywords
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