Commuting maps: a survey.
Let \(R\) be a ring and \(S\) a nonempty subset of \(R\). A map \(f\colon S\to R\) is called commuting on \(S\) if \(f(x)x=xf(x)\) for all \(x\in S\). This paper is a wide-ranging and accessible survey dealing with commuting maps and related maps on various classes of rings, including prime and semiprime rings, Banach algebras, and \(C^*\)-algebras. The major section headings are: Commuting derivations, Commuting additive maps, Commuting traces of multiadditive maps, and Applications. A huge but incomplete bibliography indicates that the area under discussion has been and continues to be a lively area of research.
scientific article; zbMATH DE number 2148903