Let A be a prime ring of characteristic not 2, with center Z A and with involution. Let S be the set of symmetric elements of A. Suppose that f : S → A is an additive map such that [f (x), f (y)] = [x, y] for all x, y ∈ S. Then unless A is an order in a 4-dimensional central simple algebra, there exists an additive map μ : S → Z (A) such that f (x) = x + μ (x) for all x ∈ S or f (x) = - x + μ (x) for all x ∈ S.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics