Abstract and Applied Analysis

Characterization of Multiplicative Lie Triple Derivations on Rings

Xiaofei Qi

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Abstract

Let R be a ring having unit 1. Denote by Z R the center of R . Assume that the characteristic of R is not 2 and there is an idempotent element e R such that a R e = 0 a = 0   and   a R 1 - e = 0 a = 0 . It is shown that, under some mild conditions, a map L : R R is a multiplicative Lie triple derivation if and only if L x = δ x + h x for all x R , where δ : R R is an additive derivation and h : R Z R is a map satisfying h a , b , c = 0 for all a , b , c R . As applications, all Lie (triple) derivations on prime rings and von Neumann algebras are characterized, which generalize some known results.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 739730, 10 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412277100

Digital Object Identifier
doi:10.1155/2014/739730

Mathematical Reviews number (MathSciNet)
MR3232862

Zentralblatt MATH identifier
07022987

Citation

Qi, Xiaofei. Characterization of Multiplicative Lie Triple Derivations on Rings. Abstr. Appl. Anal. 2014 (2014), Article ID 739730, 10 pages. doi:10.1155/2014/739730. https://projecteuclid.org/euclid.aaa/1412277100


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