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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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/871 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-8712018-03-21T12:35:55Z On one-sided Lie nilpotent ideals of associative rings Luchko, Victoriya S. Petravchuk, Anatoliy P. associative ring, one-sided ideal, Lie nilpotent ideal, derived length 16D70 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. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/871 Algebra and Discrete Mathematics; Vol 6, No 4 (2007) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/871/401 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-03-21T12:35:55Z |
| collection |
OJS |
| language |
English |
| topic |
associative ring one-sided ideal Lie nilpotent ideal derived length 16D70 |
| spellingShingle |
associative ring one-sided ideal Lie nilpotent ideal derived length 16D70 Luchko, Victoriya S. Petravchuk, Anatoliy P. On one-sided Lie nilpotent ideals of associative rings |
| topic_facet |
associative ring one-sided ideal Lie nilpotent ideal derived length 16D70 |
| format |
Article |
| author |
Luchko, Victoriya S. Petravchuk, Anatoliy P. |
| author_facet |
Luchko, Victoriya S. Petravchuk, Anatoliy P. |
| author_sort |
Luchko, Victoriya S. |
| title |
On one-sided Lie nilpotent ideals of associative rings |
| title_short |
On one-sided Lie nilpotent ideals of associative rings |
| title_full |
On one-sided Lie nilpotent ideals of associative rings |
| title_fullStr |
On one-sided Lie nilpotent ideals of associative rings |
| title_full_unstemmed |
On one-sided Lie nilpotent ideals of associative rings |
| title_sort |
on one-sided lie nilpotent ideals of associative rings |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/871 |
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AT luchkovictoriyas ononesidedlienilpotentidealsofassociativerings AT petravchukanatoliyp ononesidedlienilpotentidealsofassociativerings |
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2025-07-17T10:36:41Z |
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2025-07-17T10:36:41Z |
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1837890117994283008 |