Zagreb Workshop on Operator Theory

Commuting maps of triangular rings

A map $F:R \to R$ of a ring $R$ is called commuting if $F(x)x-xF(x)=0$ for all $x\in R$. We consider the problem of describing the form of commuting additive maps of triangular rings. Using the notion of the maximal left ring of quotients we generalize Cheung's result on commuting maps and we also consider functional identities of degree 2 on triangular rings.