Derivations and centralizing mappings in prime rings
Journal
Taiwanese Journal of Mathematics
Journal Volume
1
Journal Issue
3
Pages
333-342
Date Issued
1997
Author(s)
Abstract
Let R be a prime ring with extended centroid C and ρ a nonzero right ideal of R. In this paper we investigate the derivations δ, d on R such that [δ(x), d(x)] ε C for all x ε ρ. As an application, we prove that any centralizing additive mapping f on ρ must be of the form f(x) = λx + μ(x) for all x ε ρ, where λ ε C and μ : ρ → C, except when [ρ, ρ]ρ = 0.
Type
journal article