Abstract
Let A be a prime ring and let R be a noncentral Lie ideal of A. An additive map f : R → A is called strong commutativity preserving (SCP) on R if [f (x), f (y)] = [x, y] for all x, y ∈ R. In this paper we show that if f is SCP on R, then there exist λ ∈ C, λ2 = 1 and an additive map μ : R → Z (A) such that f (x) = λ x + μ (x) for all x ∈ R where C is the extended centroid of A, unless charA = 2 and A satisfies the standard identity of degree 4.
Original language | English |
---|---|
Pages (from-to) | 1601-1609 |
Number of pages | 9 |
Journal | Linear Algebra and Its Applications |
Volume | 428 |
Issue number | 7 |
DOIs | |
Publication status | Published - 2008 Apr 1 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics