Let F be a field and let Mn(F) be the ring of all n×n matrices over F, where n≥2 is an integer. We characterize additive maps f:Mn(F)→Mn(F) satisfying f(x)xm=xmf(x) for all invertible (singular) x∈Mn(F), where m≥2 is an integer.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics