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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A Lie property in group rings


Authors: Antonino Giambruno and Sudarshan K. Sehgal
Journal: Proc. Amer. Math. Soc. 105 (1989), 287-292
MSC: Primary 16A68; Secondary 16A27, 16A70
MathSciNet review: 929415
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Abstract: Let $ A$ be an additive subgroup of a group ring $ R$ over a field $ K$. Denote by $ [A,R]$ the additive subgroup generated by the Lie products $ [a,r] = ar - ra,a \in A,r \in R$. Inductively, let $ [A,{R_n}] = [[A,{R_{n - 1}}],R]$. We prove that $ [A,{R_n}] = 0$ for some $ n \Rightarrow [A,R]R$ is a nilpotent ideal.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0929415-5
PII: S 0002-9939(1989)0929415-5
Article copyright: © Copyright 1989 American Mathematical Society