DOI QR코드

DOI QR Code

GENERALIZED DERIVATIONS AND DERIVATIONS OF RINGS AND BANACH ALGEBRAS

  • 투고 : 2013.07.24
  • 심사 : 2013.11.15
  • 발행 : 2013.12.25

초록

We investigate anti-centralizing and skew-centralizing mappings involving generalized derivations and derivations on prime and semiprime rings. We also obtain some range inclusion results for generalized linear derivations and linear derivations on Banach algebras by applying the algebraic techniques. Some results in this note are to improve the ones in [22].

키워드

참고문헌

  1. K.I. Beidar, Rings of quotients of semiprime rings, Vestnik Moskov. Univ. Ser I Mat. Meh. (Engl. Transl. Moscow Univ. Math. Bull.) 33 (1978), 36-42.
  2. M. Bresar, On skew-commuting mappings of rings, Bull. Austral. Math. Soc. 47 (1993), 291-296. https://doi.org/10.1017/S0004972700012521
  3. M. Bresar, On the distance of the compositions of two derivations to the generalized derivations, Glasgow Math. J. 33 (1991), 89-93. https://doi.org/10.1017/S0017089500008077
  4. M. Bresar and J. Vukman, Derivations of noncommutative Banach algebras, Arch. Math. 59 (1992), 363-370. https://doi.org/10.1007/BF01197053
  5. L.-O. Chung and J. Luh, Semiprime rings with nilpotent derivations, Canad. Math. Bull. 24 (1981), 415-421. https://doi.org/10.4153/CMB-1981-064-9
  6. J. Cusack, Automatic continuity and topologically simple radical Banach algebras, J. London Math. Soc. 16(2) (1977), 493-500.
  7. Q. Deng and H. E. Bell, On derivations and commutativity in semiprime rings, Comm. Algebra 23 (1995), 3705-3713. https://doi.org/10.1080/00927879508825427
  8. R.V. Garimella, Continuity of derivations on some semiprime Banach algebras, Proc. Amer. Math. Soc. 66(22) (1987), 289-292.
  9. B. Hvala, Generalized derivations in rings, Comm. Algebra 26(4) (1998), 1147-1166. https://doi.org/10.1080/00927879808826190
  10. T.-K. Lee, Semiprime rings with dierential identities, Bull. Inst. Math. Acad. Sinica 20 (1992), 27-38.
  11. T.-K. Lee, Generalized derivations of left faithful rings, Comm. Algebra 27(8) (1999), 4057-4073. https://doi.org/10.1080/00927879908826682
  12. M. Mathieu and V. Runde, Derivations mapping into the radical II, Bull. London Math. Soc. 24 (1992), 485-487. https://doi.org/10.1112/blms/24.5.485
  13. E. Posner, Derivations in Prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1102.
  14. M. A. Quadri, M. Shadab Khan and N. Rehman, Generalized derivations and commutativity of prime rings, Indian J. pure appl. Math. 34(9) (2003), 1393-1396.
  15. C.E. Rickart. General theory of Banach algebra, Van Nostrand, Princeton (1950).
  16. A. M. Sinclair, Continuous derivations on Banach algebras, Proc. Amer. Math. Soc. 20 (1969), 166-170.
  17. A. M. Sinclair, Automatic continuity of linear operators, London Math. Soc. Lecture Note Ser. 21, 1976.
  18. I.M. Singer and J. Wermer, Derivations on commutative normed algebras, Math. Ann. 129 (1955), 435-460.
  19. M.P. Thomas, The image of a derivation is contained in the radical, Annals of Math. 128 (1988), 435-460. https://doi.org/10.2307/1971432
  20. M.P. Thomas, Primitive ideals and derivations on noncommutative Banach algebras, Pacic. J. Math.159 (1993), 139-152. https://doi.org/10.2140/pjm.1993.159.139
  21. J. Vukman, Identities with derivations on rings and Banach algebras, Glas. Mat. Ser. III, 40 (2005), 189-199. https://doi.org/10.3336/gm.40.2.01
  22. F. Wei and Z. Xiao, Pair of (generalized-)derivations on rings and Banach algebras, Bull. Korean Math. Soc. 46(5) (2009), 857-866. https://doi.org/10.4134/BKMS.2009.46.5.857