On Hersteinʹs Lie Map Conjectures, III

In the two papers, “On Hersteinʹs Lie Map Conjectures, I and II,” solutions of all of Hersteinʹs problems concerning Lie isomorphisms and derivations were given under the assumption that the algebras involved were of “sufficiently high” dimension. In the present paper we remove this restriction, thereby solving Hersteinʹs problems in full generality.