This article is cited 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.

MSC: 16D70

Language: English

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