Bi-additive maps of �i-Lie product type vanishing on zero products of XY and YX
Journal
Communications in Algebra
Journal Volume
45
Journal Issue
8
Pages
3449-3467
Date Issued
2017
Author(s)
Abstract
We study bi-additive maps of ξ-Lie product type satisfying certain local property from the viewpoint of functional identities. Let R be a unital prime ring with extended centroid C, ξ∈C, and maximal left ring of quotients Qml(R). Suppose that R contains a nontrivial idempotent. We completely characterize additive maps ϕ:R→Qml(R) having the property that [φ(x), y]ξ + [x, φ(y)]ξ = 0 whenever x,y∈R satisfy xy = 0 = yx. As consequences, some known results are fully generalized.
Type
journal article