B-generalized derivations of semiprime rings having nilpotent values
Journal
Journal of the Australian Mathematical Society
Journal Volume
96
Journal Issue
3
Pages
326-337
Date Issued
2014
Author(s)
Tamer Koşan, M.
Abstract
Let R be a semiprime ring with extended centroid C and with maximal right ring of quotients Qmr (R). Let d: R → Qmr (R) be an additive map and b σ Qmr (R). An additive map δ R → Qmr (R) is called a (left) b-generalized derivation with associated map d if δ(xy) = δ(x)y + bxd(y) for all x; y σ R. This gives a unified viewpoint of derivations, generalized derivations and generalized σ-derivations with an X-inner automorphism σ. We give a complete characterization of b-generalized derivations of R having nilpotent values of bounded index. This extends several known results in the literature. Copyright © 2014 Australian Mathematical Publishing Association Inc.
Type
journal article