On rings for which homogeneous maps are linear

Abstract:

Let $R$ be the collection of all rings $R$ such that for every $R$-module $G$, the centralizer near-ring ${M_R}(G) = \{ f:G \to G|f(rx) = rf(x),r \in R,x \in G\}$ is a ring. We show $R \in R$ if and only if ${M_R}(G) = {\text {En}}{{\text {d}}_R}(G)$ for each $R$-module $G$. Further information about $R$ is collected and the Artinian rings in $R$ are completely characterized.