DOI QR코드

DOI QR Code

Annihilating Conditions of Generalized Skew Derivations on Lie Ideals

  • Nadeem ur Rehman (Department of Mathematics, Aligarh Muslim University) ;
  • Sajad Ahmad Pary (Department of Mathematics, Aligarh Muslim University) ;
  • Junaid Nisar (Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed) University)
  • 투고 : 2022.03.29
  • 심사 : 2022.08.22
  • 발행 : 2023.09.30

초록

Let 𝔄 be a prime ring of char(𝔄 ≠ 2, ℒ a non-central Lie ideal of 𝔄, ℱ a generalized skew derivation of 𝔄 and p ∈ 𝔄, a nonzero fixed element. If pℱ(η)η ∈ C for any η ∈ ℒ, then 𝔄 satisfies S4.

키워드

과제정보

The authors are greatly indebted to the referee for his/her constructive comments and suggestions, which improved the quality of the paper.

참고문헌

  1. C. Abdioglu and T. K. Lee, A basic functional identity with application to jordan σ-biderivations, comm. Algebra, 45(4)(2017), 1741-1756  https://doi.org/10.1080/00927872.2016.1222413
  2. K. I. Beidar and M. Bresar, Extended Jacobson density theorem for rings with automorphisms and derivations, Israel J. Math., 122(2001), 317-346.  https://doi.org/10.1007/BF02809906
  3. J. Bergen, I. N. Herstein and J. W. Kerr, Lie ideals and derivations of prime rings, J. Algebra, 71(1981), 259-267.  https://doi.org/10.1016/0021-8693(81)90120-4
  4. C. M. Chang and T. K. Lee, Annihilators of power values of derivations in prime rings, Comm. Algebra, 26(7)(1998), 2091-2113.  https://doi.org/10.1080/00927879808826263
  5. C. L. Chuang, GPIs having coefficients in Utumi quotient rings, Proc. Amer. Math. Soc., 103(3)(1988), 723-728.  https://doi.org/10.1090/S0002-9939-1988-0947646-4
  6. C. L. Chuang, Differential identities with automorphism and anti-automorphisms II, J. Algebra, 160(1993), 292-335.  https://doi.org/10.1006/jabr.1993.1181
  7. C. L. Chuang and T. K. Lee, Identities with a single skew derivation, J. Algebra, 288(1)(2005), 59-77.  https://doi.org/10.1016/j.jalgebra.2003.12.032
  8. B. Dhara and V. De Filippis, Notes on generalized derivation on Lie ideals in prime rings, Bull. Korean Math. Soc., 46(3)(2009), 599-605.  https://doi.org/10.4134/BKMS.2009.46.3.599
  9. Y. Du and Y. Wang, A result on generalized derivations in prime rings, Hacet. J. Math. Stat., 42(1)(2013), 81-85. 
  10. N. Jacobson, Structure of rings, Amer. Math. Soc. Colloquium Publications, vol. 37, (1964). 
  11. C. Lanski and S. Montgomery, Lie structure of prime ring of characteristic 2, Pacific J. Math., 42(1)(1972), 117-136.  https://doi.org/10.2140/pjm.1972.42.117
  12. W. S. Martindale III, Prime rings satisfying a generalized polynomial identity, J. Algebra, 12(1969), 576-584.  https://doi.org/10.1016/0021-8693(69)90029-5
  13. R. K. Sharma and B. Dhara, An annihilator condition on prime rings with derivations, Tamsui Oxf. J. Math. Sci., 21(1)(2005), 71-80.  https://doi.org/10.5486/PMD.2007.3516
  14. Y. Wang, Power-centralizing automorphisms of Lie ideals in prime rings, Comm. Algebra, 34(2)(2006), 609-615. https://doi.org/10.1080/00927870500387812