DOI QR코드

DOI QR Code

GENERALIZED DERIVATIONS WITH ANNIHILATOR CONDITIONS IN PRIME RINGS

  • Wang, Yu (Mathematics and Science College Shanghai Normal University)
  • 투고 : 2009.11.18
  • 발행 : 2011.09.30

초록

Let R be a prime ring, H a generalized derivation of R, L a noncentral Lie ideal of R, and 0 ${\neq}$ a ${\in}$ R. Suppose that $au^sH(u)u^t$ = 0 for all u ${\in}$ L, where s; t ${\geq}$ 0 are fixed integers. Then H = 0 unless satisfies $S_4$, the standard identity in four variables.

키워드

참고문헌

  1. E. Albas, N. Argac, and V. D. Fillippis, Generalized derivations with Engel conditions on one-sided ideals, Comm. Algebra 36 (2008), no. 6, 2063-2071. https://doi.org/10.1080/00927870801949328
  2. A. A. Albert and B. Muckenhoupt, On matrices of trace zero, Michigan Math. J. 4 (1957), 1-3. https://doi.org/10.1307/mmj/1028990168
  3. K. I. Beidar, W. S. Martindale III, and A. V. Mikhalev, Rings with Generalized Identi- ties, Marcel Dekker, New York-Basel-Hong Kong, 1996.
  4. C. L. Chuang, GPIs having coefficients in Utumi quotient rings, Proc. Amer. Math. Soc. 103 (1988), no 3, 723-728. https://doi.org/10.1090/S0002-9939-1988-0947646-4
  5. B. Dhara and V. De Filippis, Notes on generalized derivations on Lie ideals in prime rings, Bull. Korean Math. Soc. 46 (2009), no. 3, 599-605. https://doi.org/10.4134/BKMS.2009.46.3.599
  6. B. Dhara and R. K. Sharma, Derivations with annihilator conditions in prime rings, Publ. Math. Debrecen 71 (2007), no. 1-2, 11-20.
  7. T. 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. Hungar 14 (1963), 369-371. https://doi.org/10.1007/BF01895723
  9. V. De Filippis, An Engel condition with generalized derivations on multilinear polyno- mials, Israel J. Math. 162 (2007), 93-108. https://doi.org/10.1007/s11856-007-0090-y
  10. V. De Filippis, Posner's second theorem and an annihilator condition with generalized deriva- tions, Turkish J. Math. 32 (2008), no. 2, 197-211.
  11. V. De Filippis, Generalized derivations in prime rings and noncommutative Banach algebras, Bull. Korean Math. Soc. 45 (2008), no. 4, 621-629. https://doi.org/10.4134/BKMS.2008.45.4.621
  12. B. Hvala, Generalized derivations in rings, Comm. Algebra 26 (1998), no. 4, 1147-1166. https://doi.org/10.1080/00927879808826190
  13. N. Jacobson, Structure of Rings, Amer. Math. Soc. Colloq. Pub., 37, Amer. Math. Soc., Providence, RI, 1964.
  14. V. K. Kharchenko, Differential identities of prime rings, Algebra Logika 17 (1978), no. 2, 220-238, 242-243.
  15. C. Lanski and S. Montgomery, Lie structure of prime rings of characteristic 2, Pacific J. Math. 42 (1972), 117-136. https://doi.org/10.2140/pjm.1972.42.117
  16. T. K. Lee, Generalized derivations of left faithful rings, Comm. Algebra 27 (1999), no. 8, 4057-4073. https://doi.org/10.1080/00927879908826682
  17. 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
  18. J. S. Lin and C. K. Liu, Generalized derivations with invertible or nilpotent on multi- linear polynomials values, Comm. Algebra 34 (2006), no. 2, 633-640. https://doi.org/10.1080/00927870500387861
  19. 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
  20. Y. Wang, Generalized derivations with power-central values on multilinear polynomials, Algebra Colloq. 13 (2006), no. 3, 405-410. https://doi.org/10.1142/S1005386706000344