A Lie property in group rings
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- by Antonino Giambruno and Sudarshan K. Sehgal PDF
- Proc. Amer. Math. Soc. 105 (1989), 287-292 Request permission
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.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 105 (1989), 287-292
- MSC: Primary 16A68; Secondary 16A27, 16A70
- DOI: https://doi.org/10.1090/S0002-9939-1989-0929415-5
- MathSciNet review: 929415