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A RESULT ON GENERALIZED DERIVATIONS WITH ENGEL CONDITIONS ON ONE-SIDED IDEALS

  • Demir, Cagri (DEPARTMENT OF MATHEMATICS SCIENCE FACULTY EGE UNIVERSITY) ;
  • Argac, Nurcan (DEPARTMENT OF MATHEMATICS SCIENCE FACULTY EGE UNIVERSITY)
  • 발행 : 2010.05.01

초록

Let R be a non-commutative prime ring and I a non-zero left ideal of R. Let U be the left Utumi quotient ring of R and C be the center of U and k, m, n, r fixed positive integers. If there exists a generalized derivation g of R such that $[g(x^m)x^n,\;x^r]_k\;=\;0$ for all x $\in$ I, then there exists a $\in$ U such that g(x) = xa for all x $\in$ R except when $R\;{\cong}\;=M_2$(GF(2)) and I[I, I] = 0.

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참고문헌

  1. E. Albas, N. Argac, and V. De Filippis, Generalized derivations with Engel conditions on one-sided ideals, Comm. Algebra 36 (2008), no. 6, 2063-2071. https://doi.org/10.1080/00927870801949328
  2. N. Argac, L. Carini, and V. De Filippis, An Engel condition with generalized derivations on Lie ideals, Taiwanese J. Math. 12 (2008), no. 2, 419-433. https://doi.org/10.11650/twjm/1500574164
  3. N. Argac, V. De Filippis, and H. G. Inceboz, Generalized derivations with power central values on multilinear poynomials on right ideals, to appear in Rendiconti di Padova,
  4. K. I. Beidar, W. S. Martindale III, and A. V. Mikhalev, Rings with Generalized Identities, Marcel Dekker, Inc., New York, 1996.
  5. M. Bresar, On generalized biderivations and related maps, J. Algebra 172 (1995), no. 3, 764-786. https://doi.org/10.1006/jabr.1995.1069
  6. C. L. Chuang, GPIs having coefficients in Utumi quotient rings, Proc. Amer. Math. Soc. 103 (1988), no. 3, 723-728. https://doi.org/10.2307/2046841
  7. J. S. Erickson, W. S. Martindale III, and J. M. Osborn, Prime nonassociative algebras, Pacific J. Math. 60 (1975), no. 1, 49-63. https://doi.org/10.2140/pjm.1975.60.49
  8. C. Faith and Y. Utumi, On a new proof of Litoff’s theorem, Acta Math. Acad. Sci. Hungar 14 (1963), 369-371. https://doi.org/10.1007/BF01895723
  9. B. Hvala, Generalized derivations in rings, Comm. Algebra 26 (1998), no. 4, 1147-1166. https://doi.org/10.1080/00927879808826190
  10. V. K. Kharchenko, Differential identities of prime rings, Algebra i Logika 17 (1978), no. 2, 220-238, 242-243.
  11. C. Lanski, An Engel condition with derivation for left ideals, Proc. Amer. Math. Soc. 125 (1997), no. 2, 339-345. https://doi.org/10.1090/S0002-9939-97-03673-3
  12. T. K. Lee, Semiprime rings with differential identities, Bull. Inst. Math. Acad. Sinica 20 (1992), no. 1, 27-38.
  13. T. K. Lee, Generalized derivations of left faithful rings, Comm. Algebra 27 (1999), no. 8, 4057-4073. https://doi.org/10.1080/00927879908826682
  14. T. K. Lee, Left annihilators characterized by GPIs, Trans. Amer. Math. Soc. 347 (1995), no. 8, 3159-3165. https://doi.org/10.2307/2154780
  15. T. K. Lee, Semiprime rings with hypercentral derivations, Canad. Math. Bull. 38 (1995), no. 4, 445-449. https://doi.org/10.4153/CMB-1995-065-2
  16. T. K. Lee, Derivations with Engel conditions on polynomials, Algebra Colloq. 5 (1998), no. 1, 13-24.
  17. T. K. Lee and W. K. Shiue, A result on derivations with Engel condition in prime rings, Southeast Asian Bull. Math. 23 (1999), no. 3, 437-446.
  18. T. K. Lee and W. K. Shiue, Identities with generalized derivations, Comm. Algebra 29 (2001), no. 10, 4437-4450. https://doi.org/10.1081/AGB-100106767
  19. P. H. Lee and T. L. Wong, Derivations cocentralizing Lie ideals, Bull. Inst. Math. Acad. Sinica 23 (1995), no. 1, 1-5.
  20. 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
  21. E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1100. https://doi.org/10.2307/2032686

피인용 문헌

  1. A Characterization of Generalized Derivations on Prime Rings vol.44, pp.8, 2016, https://doi.org/10.1080/00927872.2015.1065861
  2. Hypercentralizing generalized skew derivations on left ideals in prime rings vol.173, pp.3, 2014, https://doi.org/10.1007/s00605-013-0486-1