## Rocky Mountain Journal of Mathematics

### 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.

#### Article information

Source
Rocky Mountain J. Math., Volume 49, Number 3 (2019), 761-772.

Dates
First available in Project Euclid: 23 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1563847232

Digital Object Identifier
doi:10.1216/RMJ-2019-49-3-761

Mathematical Reviews number (MathSciNet)
MR3983299

#### Citation

Ferreira, Bruno Leonardo Macedo; Jr, Henrique Guzzo. Characterization of Lie multiplicative derivation on alternative rings. Rocky Mountain J. Math. 49 (2019), no. 3, 761--772. doi:10.1216/RMJ-2019-49-3-761. https://projecteuclid.org/euclid.rmjm/1563847232

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