A basic functional identity with applications to Jordan ?-biderivations
Journal
Communications in Algebra
Journal Volume
45
Journal Issue
4
Pages
1741-1756
Date Issued
2017
Author(s)
Abdio?lu, C.
Abstract
Let R be a noncommutative prime ring with extended centroid C and maximal left ring of quotients Qml(R). The aim of the paper is to study a basic functional identity concerning bi-additive maps on R. Precisely, it is proved that a bi-additive map B:R×R→Qml(R) satisfying [B(x,y),[x,y]] = 0 for all x,y∈R must be of the form (x,y)↦λ[x,y]+μ(x,y) for x,y∈R, where λ∈C and μ:R×R→C is a bi-additive map. As applications to the theorem, Jordan σ-biderivations with σ an epimorphism and additive commuting maps on noncommutative Lie ideals of R are characterized.
Type
journal article