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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
DOI: https://doi.org/10.1090/S0002-9939-1989-0929415-5
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.


References [Enhancements On Off] (What's this?)

  • [1] N. Gupta and F. Levin, On the Lie ideals of a ring, J. Algebra 81 (1983), 225-231. MR 696135 (84i:16036)
  • [2] S. A. Jennings, On rings whose associated Lie rings are nilpotent, Bull. Amer. Math. Soc. 53 (1947), 593-597. MR 0020984 (9:5c)
  • [3] I. B. S. Passi, D. S. Passman and S. K. Sehgal, Lie solvable group rings, Canad. J. Math. 25 (1973), 748-757. MR 0325746 (48:4092)
  • [4] D. S. Passman, The algebraic structure of group rings, Wiley, New York, 1977. MR 470211 (81d:16001)
  • [5] S. K. Sehgal, Topics in group rings, Marcel Dekker, New York, 1978. MR 508515 (80j:16001)

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DOI: https://doi.org/10.1090/S0002-9939-1989-0929415-5
Article copyright: © Copyright 1989 American Mathematical Society

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