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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.
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Matej Breˇsar (2004) studied this question.
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