Abstract and Applied Analysis

Characterization of Multiplicative Lie Triple Derivations on Rings

Xiaofei Qi

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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.

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

First available in Project Euclid: 2 October 2014

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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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