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Algebra and Discrete Mathematics, 2007, Issue 4, Pages 102–107
(Mi adm237)
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This article is cited in 1 scientific paper (total in 1 paper)
RESEARCH ARTICLE
On one-sided Lie nilpotent ideals of associative rings
Victoriya S. Luchko, Anatoliy P. Petravchuk Kiev Taras Shevchenko University, Faculty of Mechanics and Mathematics, 64, Volodymyrska street, 01033 Kyiv,
Ukraine
Abstract:
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.
Keywords:
associative ring, one-sided ideal, Lie nilpotent ideal, derived length.
Citation:
Victoriya S. Luchko, Anatoliy P. Petravchuk, “On one-sided Lie nilpotent ideals of associative rings”, Algebra Discrete Math., 2007, no. 4, 102–107
Linking options:
https://www.mathnet.ru/eng/adm237 https://www.mathnet.ru/eng/adm/y2007/i4/p102
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Abstract page: | 149 | Full-text PDF : | 61 | First page: | 1 |
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