One of the most studied linear preserver problems is the problem of characterizing maps preserving commutativity. In this paper we study maps preserving commutativity on a Lie ideal L of a prime algebra A. We show by an example that in general we cannot expect the same standard conclusion as in the case when L=A. Therefore we confine ourselves to some special classes of algebras where the usual result can be proved.
- Commutativity-preserving maps
- Lie ideal
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics