Commutativity preservers via maximal centralizers (Q2875444)

Over the past 40 years, there has been a lot of work done concerning transformations on matrix algebras and on operator algebras preserving commutativity. The present paper contributes to this research. Here, the authors deal with non-linear bijective maps on \(n\times n\) matrices over a field. They describe the precise structure of such maps on the set of all diagonal and all rank-one matrices assuming \(n\geq 3\) and the underlying field has at least \(2^{n-1}\) elements.