Derivations satisfying certain algebraic identities on Lie ideals
Let d be a derivation of a semiprime ring R and L a nonzero Lie ideal of R. In this note, it is proved that every noncentral square-closed Lie ideal of R contains a nonzero ideal of R. Further, we use this result to characterize the conditions: d(xy) = d(x)d(y), d(xy) = d(y)d(x) on L. With this, a t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Kragujevac, Faculty of Technical Sciences Čačak, Serbia
2019-01-01
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| Series: | Mathematica Moravica |
| Subjects: | |
| Online Access: | https://scindeks-clanci.ceon.rs/data/pdf/1450-5932/2019/1450-59321902079S.pdf |
| Summary: | Let d be a derivation of a semiprime ring R and L a nonzero Lie ideal of R. In this note, it is proved that every noncentral square-closed Lie ideal of R contains a nonzero ideal of R. Further, we use this result to characterize the conditions: d(xy) = d(x)d(y), d(xy) = d(y)d(x) on L. With this, a theorem of Ali et al. [14] can be deduced. |
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| ISSN: | 1450-5932 2560-5542 |