On one-sided Lie nilpotent ideals of associative rings
We prove that a Lie nilpotent one-sided ideal of an associative ring \(R\) is contained in a Lie solvable two-sided ideal of \(R\). An estimation of derived length of such Lie solvable ideal is obtained depending on the class of Lie nilpotency of the Lie nilpotent one-sided ideal of \(R.\) One-si...
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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/871 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | We prove that a Lie nilpotent one-sided ideal of an associative ring \(R\) is contained in a Lie solvable two-sided ideal of \(R\). An estimation of derived length of such Lie solvable ideal is obtained depending on the class of Lie nilpotency of the Lie nilpotent one-sided ideal of \(R.\) One-sided Lie nilpotent ideals contained in ideals generated by commutators of the form \([\ldots [ [r_1, r_{2}], \ldots ], r_{n-1}], r_{n}]\) are also studied. |
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