Rocky Mountain Journal of Mathematics

Characterization of Lie multiplicative derivation on alternative rings

Bruno Leonardo Macedo Ferreira and Henrique Guzzo Jr

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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

Subjects
Primary: 17A36: Automorphisms, derivations, other operators 17D05: Alternative rings

Keywords
Lie multiplicative derivation prime alternative rings

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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References

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