Let D be a division ring and let Mn(D) be the ring of all n×n matrices over D with center Z, where n≥2 is an integer. We describe the additive map f: Mn (D)→ Mn (D) such that f(x)x-xf(x)∈Z for all invertible (singular) x∈Mn(D).
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics