Characterization of Lie multiplicative derivation on alternative rings

Abstract

In this paper, we generalize the result valid for associative rings Bresar and Martindale III to alternative rings. Let $\mathfrak{R} $ be a unital alternative ring, and $\mathfrak{D} \colon \mathfrak{R} \rightarrow \mathfrak{R} $ is a Lie multiplicative derivation. Then, $\mathfrak{D} $ is the form $\delta + \tau $, where $\delta $ is an additive derivation of $\mathfrak{R} $ and $\tau $ is a map from $\mathfrak{R} $ into its center $\mathcal {\mathfrak{R} }$, which maps commutators into the zero.