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On associative algebras satisfying the Engel condition

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Abstract

It is shown that every finitely generated associative algebra over a field of characteristicp>0 satisfying the Engel condition is Lie-nilpotent. It follows that the Engel condition is inherited from an algebraA to its group of units,U(A).

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References

  1. S. A. Amitsur,On rings with identities, J. London Math. Soc.30 (1955), 464–470.

    Article  MATH  MathSciNet  Google Scholar 

  2. J. A. Bahturin,Lectures on Lie Algebras, Akademik-Verlag, Berlin, 1978.

    MATH  Google Scholar 

  3. A. Braun,Lie rings and the Engel condition, J. Algebra31 (1974), 287–292.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Braun,The nilpotency of the radical in a finitely generated PI-ring, J. Algebra89 (1984), 375–396.

    Article  MATH  MathSciNet  Google Scholar 

  5. P. M. Cohn,A non-nilpotent Lie ring satisfying the Engel condition and a non-nilpotent Engel group, Proc. Camb. Phil. Soc.51 (1955), 401–405.

    MATH  Google Scholar 

  6. K. W. Gruenberg,Two theorems on Engel groups, Proc. Camb. Phil. Soc.49 (1953), 377–380.

    Article  MATH  MathSciNet  Google Scholar 

  7. N. D. Gupta and F. Levin,On the Lie ideals of a ring, J. Algebra81 (1983), 225–231.

    Article  MATH  MathSciNet  Google Scholar 

  8. P. J. Higgins,Lie rings satisfying the Engel condition, Proc. Camb. Phil. Soc.50 (1954), 8–15.

    MATH  MathSciNet  Google Scholar 

  9. A. I. Kostrikin,On the Burnside problem, Izv. Akad. Nauk SSSR, Ser. Mat.23, No. 1 (1959), 3–34.

    MATH  MathSciNet  Google Scholar 

  10. A. I. Kostrikin,Around Burnside, Nauka, Moscow, 1986.

    MATH  Google Scholar 

  11. Y. P. Razmyslov,On Lie algebras satisfying the Engel condition, Algebra and Logic10, No. 5 (1971), 21–29.

    Article  MATH  MathSciNet  Google Scholar 

  12. L. W. Rowen,Polynomial Identities in Ring Theory, Academic Press, New York, 1980.

    MATH  Google Scholar 

  13. E. I. Zel’manov,On Engel Lie algebras, Sib. Mat. J.29, No. 5 (1988), 112–117.

    MathSciNet  Google Scholar 

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Shalev, A. On associative algebras satisfying the Engel condition. Israel J. Math. 67, 287–290 (1989). https://doi.org/10.1007/BF02764947

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  • DOI: https://doi.org/10.1007/BF02764947

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