The additive group of a Lie nilpotent associative ring

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• 作者：Alexei Krasilnikov
• 关键词：16R10 ; 16R40
• 刊名：Journal of Algebra
• 出版年：2013
• 出版时间：15 October, 2013
• 年：2013
• 卷：392
• 期：Complete
• 页码：10-22
• 全文大小：284 K

文摘

Let be the free unital associative ring freely generated by an infinite countable set . Define a left-normed commutator by , . For , let be the two-sided ideal in generated by all commutators . It can be easily seen that the additive group of the quotient ring is a free abelian group. Recently Bhupatiraju, Etingof, Jordan, Kuszmaul and Li have noted that the additive group of is also free abelian. In the present note we show that this is not the case for . More precisely, let be the ideal in generated by together with all elements . We prove that is a non-trivial elementary abelian 3-group and the additive group of is free abelian.