COMMUTING MAPS: A SURVEY

A map f on a ring A is said to be commuting if f(x) commutes with x for every x ∈ A. The paper surveys the development of the theory of commuting maps and their applications. The following topics are discussed: commuting derivations, commuting additive maps, commuting traces of multiadditive maps, various generalizations of the notion of a commuting map, and applications of results on commuting maps to different areas, in particular to Lie theory.