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Generalized Jordan derivations on semiprime rings

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Abstrakty
EN
It is shown that, given a 2-torsion-free semiprime ring with unit e, every generalized Jordan derivation on R is a generalized derivation. Let n be a fixed positive integer, R be a noncommutative (n+1)!-torsion-free prime ring with the center CR. It is proved that, if [..]: R -> R is a generalized Jordan derivation of R such that [..](x)xn + x [...].
Wydawca
Rocznik
Strony
789--798
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
autor
  • Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, P. R. China, daoshu@bit.edu.cn
Bibliografia
  • [1] E. Albas and N. Argac, Generalized derivations of prime rings, Algebra Colloq., 11 (2004), 399-410.
  • [2] N. Argac and E. Albas, On generalized (σ, τ)-derivations, Siberian Math. J., 43 (2002), 977-984.
  • [3] N. Argac, On prime and semiprime rings with derivations, Algebra Colloq., 13 (2006), 371-380.
  • [4] P. Ara and M. Mathieu, Local Multipliers of C* - Algebras, Springer Monographs in Mathematics, Springer-Verlag, London, 2003.
  • [5] 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.
  • [6] K. I. Beidar, W. S. Martindale 3rd and A. V. Mikhalev, Rings with Generalized Identities, Monographs and Textbooks in Pure and Applied Mathematics, V. 196, Marcel Dekker, New York-Basel-Hong Kong, 1996.
  • [7] M. Brešar, Jordan derivations on semiprime rings, Proc. Amer. Math. Soc., 104 (1988), 1003-1006.
  • [8] M. Brešar, On the distance of the composition of two derivations to the generalized derivations, Glasgow Math. J., 33 (1991), 89-93.
  • [9] L. O. Chung and J. Luh, Semiprime rings with nilpotent derivations, Canad. Math. Bull.,24 (1981), 415-421.
  • [10] B. Hvala, Generalized derivations in rings, Comm. Algebra, 26 (1998), 1147-1166.
  • [11] W. Jing and S. Lu, Generalized Jordan derivations on prime rings and standard operator algebras, Taiwanese J. Math., 7 (2003), 605-613.
  • [12] B. E. Johnson and A. M. Sinclair, Continuity of derivations and a problem of Kaplansky, Amer. J. Math., 90 (1968), 1067-1073.
  • [13] T. K. Lee, Semiprime rings with differential identities, Bull. Inst. Math. Acad. Sinica, 20 (1992), 27-38.
  • [14] T. K. Lee, Generalized derivations of left faithful rings, Comm. Algebra, 27 (1999), 4057-4073.
  • [15] A. Nakajima, On generalized higher derivations, Turk. J. Math., 24 (2000), 295-311.
  • [16] A. Nakajima, Generalized Jordan derivations, Proceedings of the 3rd Korea-China-Japan International Symposium on Ring Theory, Trends in Mathematics, 235-243, Birkhäuser, Boston, 2001.
  • [17] E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957), 1093-1100.
  • [18] A. M. Sinclair, Jordan homomorphisms and v on semisimple Banach algebras, Proc. Amer. Math. Soc., 24 (1970), 209-214.
  • [19] F. Wei, Pair of derivations on rings and Banach algebras, Aequationes Math., in press.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA5-0022-0005
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