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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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

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

First available in Project Euclid: 23 July 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

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

Lie multiplicative derivation prime alternative rings


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.

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  • K.I. Beĭdar, A.V. Mikhalëv and A.M. Slinko, A primality criterion for nondegenerate alternative and Jordan algebras, Trudy Mosk. Mat. Obshch. 50 (1987), 130–137 (in Russian), Trans. Moscow Math. Soc. 261 (1988), 129–137 (in English).
  • M. Brešar, Commuting traces of biadditive mappings, commutativity-preserving mappings and Lie mappings, Trans. Amer. Math. Soc. 335 (1993), 525–546.
  • B.L.M. Ferreira and H. Guzzo, Lie maps on alternative rings, arXiv:1802.04324v1 (2018).
  • J.C.M. Ferreira and B.L.M. Ferreira, Additivity of $n$-multiplicative maps on alternative rings, Comm. Algebra 44 (2016), 1557–1568.
  • I.R. Hentzel, E. Kleinfeld and H.F. Smith, Alternative rings with idempotent, J. Algebra 64 (1980), 325–335.
  • F. Lu and B. Liu, Lie derivable maps on B(X), J. Math. Anal. Appl. 372 (2010), 369–376.
  • W.S. Martindale, III, Lie derivations of primitive rings, Michigan Math. J. 11 (1964), 183–187.
  • R.D. Schafer, An introduction to nonassociative algebras, Pure Appl. Math. 22 (1966).
  • M. Slater, Prime alternative rings, I, J. Algebra 15 (1970), 229–243.