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A note on automorphisms of lie ideals in prime rings

  • Bijan Davvaz EMAIL logo and Mohd Arif Raza
Published/Copyright: October 20, 2018
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 68 Issue 5

Abstract

In the present paper, we prove that a prime ring R with center Z satisfies s4, the standard identity in four variables if R admits a non-identity automorphism σ such that (uσ,u]vσ+vσ[uσ,u])n∈Z for all u,v in some non-central Lie ideal L of R whenever either char(R)>n or char(R)=0, where n is a fixed positive integer.

MSC 2010: Primary 16N60, 16W20; Secondary 16R50
Keywords: prime ring; automorphism; maximal right; ring of quotients; generalized polynomial identity (GPI); Lie ideal

  1. Communicated by Miroslav Ploščica

Acknowledgement

The authors would like to thank the reviewers for their suggestions.

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Received: 2016-05-21
Accepted: 2017-10-18
Published Online: 2018-10-20
Published in Print: 2018-10-25

© 2018 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2017-0179
Keywords for this article
prime ring; automorphism; maximal right; ring of quotients; generalized polynomial identity (GPI); Lie ideal

Articles in the same Issue

  1. Prof. RNDr. Beloslav Riečan, DrSc., Dr.h.c. *NOV. 10, 1936 – †AUG. 13, 2018
  2. On the n × n × n Rubik's Cube
  3. Congruences involving alternating harmonic sums modulo pαqβ
  4. On the proximity of large primes
  5. On the factorizations of cubic polynomials with the same discriminant modulo a prime
  6. Some results on abstract convexity of functions
  7. Remarks on b-Metric and metric-preserving functions
  8. Generalization of Ostrowski inequality for convex functions
  9. On microscopic sets and Fubini Property in all directions
  10. New subfamily of meromorphic multivalent starlike functions in circular domain involving q-differential operator
  11. Application of tan(φ(ξ)/2)-expansion method to burgers and foam drainage equations
  12. Approximate sentinels for diffusion phenomena with pollution
  13. Remarks on a semilinear system in ℝn motivated by difference equations
  14. Oscillation tests for difference equations with several non-monotone deviating arguments
  15. On the regularity of one-sided fractional maximal functions
  16. A note on a Banach’s fixed point theorem in b-rectangular metric space and b-metric space
  17. A note about Volterra operator
  18. Some reverse and numerical radius inequalities
  19. A class of four-dimensional CR submanifolds in six dimensional nearly Kähler manifolds
  20. Sequential decreasing strong size properties
  21. Approximation of Information Divergences for Statistical Learning with Applications
  22. Wigner's theorem for an infinite set
  23. A note on automorphisms of lie ideals in prime rings
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