Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON NAGATA-HIGMAN THEOREM

  • Lee, Woo (Department of Telecommunications, Gwangju University)
  • Published : 2009.09.30
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Abstract

Nagata[3] and Higman[1] showed that nil-algebra of the nilindex n is nilpotent of finite index. In this paper we show that the bounded degree of the nilpotency is less than or equal to $2^n-1$. Our proof needs only some elementary fact about Vandermonde determinant, which is much simpler than Nagata's or Higman's proof.

Keywords

References

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  3. M. Nagata. On the nilpotency of nil-algebras, J. Math. Soc. Japan 4(1953), 296-301. https://doi.org/10.2969/jmsj/00430296
  4. Y. P. Razmyslov. Trace identities of full matrix algebras over a field of characteristic zero, Izv. Akad. Nauk SSSR 38 (1974), 723-756
  5. Y. P. Razmyslov. Trace identities of full matrix algebras over a field of characteristic zero, English transl., Math. USSR-Izv. 8 (1974), 727-760. https://doi.org/10.1070/IM1974v008n04ABEH002126