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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| Format: | Article |
| Language: | English |
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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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| author | Xiaofei Qi |
| author_facet | Xiaofei Qi |
| author_sort | Xiaofei Qi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-db73e33a335d49468efa0eaa9296e359 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-db73e33a335d49468efa0eaa9296e3592025-02-03T01:21:48ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/739730739730Characterization of Multiplicative Lie Triple Derivations on RingsXiaofei Qi0Department of Mathematics, Shanxi University, Taiyuan 030006, ChinaLet 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.http://dx.doi.org/10.1155/2014/739730 |
| spellingShingle | Xiaofei Qi Characterization of Multiplicative Lie Triple Derivations on Rings Abstract and Applied Analysis |
| title | Characterization of Multiplicative Lie Triple Derivations on Rings |
| title_full | Characterization of Multiplicative Lie Triple Derivations on Rings |
| title_fullStr | Characterization of Multiplicative Lie Triple Derivations on Rings |
| title_full_unstemmed | Characterization of Multiplicative Lie Triple Derivations on Rings |
| title_short | Characterization of Multiplicative Lie Triple Derivations on Rings |
| title_sort | characterization of multiplicative lie triple derivations on rings |
| url | http://dx.doi.org/10.1155/2014/739730 |
| work_keys_str_mv | AT xiaofeiqi characterizationofmultiplicativelietriplederivationsonrings |