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The radical of a modular alternative loop algebra


Author: Edgar G. Goodaire
Journal: Proc. Amer. Math. Soc. 123 (1995), 3289-3299
MSC: Primary 17D05; Secondary 16S34, 20N05
DOI: https://doi.org/10.1090/S0002-9939-1995-1283551-8
MathSciNet review: 1283551
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Abstract: If G is a group of order $ {2^n}$ and F is a field of characteristic 2, it is well known that the augmentation ideal of the group algebra FG is nilpotent. In this paper, we extend this result to alternative loop algebras.


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

  • [1] R. H. Bruck, Some results in the theory of linear nonassociative algebras, Trans. Amer. Math. Soc. 56 (1944), 141-199. MR 0011083 (6:116b)
  • [2] -, A survey of binary systems, Ergeb. Math. Grenzgeb., vol. 20, Springer-Verlag, Berlin, 1958. MR 0093552 (20:76)
  • [3] Orin Chein, Moufang loops of small order, Mem. Amer. Math. Soc. 197 (1978), no. 13. MR 0466391 (57:6271)
  • [4] Orin Chein and Edgar G. Goodaire, Loops whose loop rings are alternative, Comm. Algebra 14 (1986), 293-310. MR 817047 (87c:20116)
  • [5] -, Loops whose loop rings in characteristic 2 are alternative, Comm. Algebra 18 (1990), 659-688. MR 1052760 (91g:20099)
  • [6] Orin Chein and D. A. Robinson, An "extra" law for characterizing Moufang loops, Proc. Amer. Math. Soc. 33 (1972), 29-32. MR 0292987 (45:2068)
  • [7] Edgar G. Goodaire, Alternative loop rings, Publ. Math. Debrecen 30 (1983), 31-38. MR 733069 (85k:20200)
  • [8] Edgar G. Goodaire and M. M. Parmenter, Semi-simplicity of alternative loop rings, Acta Math. Hungar. 50 (1987), 241-247. MR 918159 (89e:20119)
  • [9] S. A. Jennings, The structure of the group ring of a p-group over a radical field, Trans. Amer. Math. Soc. 50 (1941), 175-185. MR 0004626 (3:34f)
  • [10] E. Kleinfeld, A characterization of the Cayley numbers, Studies in Modern Algebra (A. A. Albert, ed.), Studies in Math., vol. 2, Math. Assoc. Amer., Washington, DC, 1963, pp. 126-143.
  • [11] H. O. Pflugfelder, Quasigroups and loops: Introduction, Heldermann Verlag, Berlin, 1990. MR 1125767 (93g:20132)
  • [12] K. A. Zhevlakov, A. M. Slin'ko, I. P. Shestakov, and A. I. Shirshov, Rings that are nearly associative (translated by Harry F. Smith), Academic Press, New York, 1982. MR 668355 (83i:17001)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1283551-8
Article copyright: © Copyright 1995 American Mathematical Society

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