Let Mn(D) be the ring of all n×n matrices over a division ring D, where n≥2 is an integer and let GLn(D) be the set of all invertible matrices in Mn(D). We describe maps f:GLn(D) →Mn(D) such that [f(x),f(y)]=[x,y] for all x,yGLn(D). The analogous result for singular matrices is also obtained.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics