Characterization of Multiplicative Lie Triple Derivations on Rings
Let R be a ring having unit 1. Denote by ZR the center of R. Assume that the characteristic of R is not 2 and there is an idempotent element e∈R such that aRe=0⇒a=0 and aR1-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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/739730 |
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| Summary: | Let R be a ring having unit 1. Denote by ZR the center of R. Assume that the characteristic of R is not 2 and there is an idempotent element e∈R such that aRe=0⇒a=0 and aR1-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 Lx=δx+hx for all x∈R, where δ:R→R is an additive derivation and h:R→ZR is a map satisfying ha,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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| ISSN: | 1085-3375 1687-0409 |