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DERIVATIONS OF SEMIPRIME RINGS AND NONCOMMUTATIVE BANACH ALGEBRAS

  • Kim, Byung-Do (Department of Mathematics, Kangnung National University)
  • Published : 2002.10.01

Abstract

Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation D : A \longrightarrowA such that D($\chi$)[D($\chi$),$\chi$]D($\chi$) $\in$ rad(A) for all $\chi$ A. In this case, we have D(A) ⊆ rad(A).

References

  1. Complete Normed Algebras F.F. Bonsall;J. Duncan
  2. Arch. Math v.63 Derivations of noncommutative Banach algebras II M. Bresar https://doi.org/10.1007/BF01196299
  3. Proc. Amer. Math. Soc. v.63 no.4 Jordan derivations on semiprime rings
  4. Canad. Math. Bull v.24 no.4 Semiprime rings with nilpotent derivatives L.O. Chung;J. Luh https://doi.org/10.4153/CMB-1981-064-9
  5. Amer. J. Math. v.90 Continuity of derivations and a problem of Kaplansky B.E. Johnson;A.M. Sinclair https://doi.org/10.2307/2373290
  6. Acta Mathematical Sinica, to appear On the derivations of semiprime rings and noncommutative Banach algebras B.D. Kim https://doi.org/10.1007/s101149900020
  7. Proc. Amer. Math. Soc. v.24 Jordan homohorphisms and derivations on semisimple Banach algebras A.M. Sinclair https://doi.org/10.2307/2036730
  8. Math. Ann v.129 Derivations on commutative normed algebras I.M. Singer;J. Wermer https://doi.org/10.1007/BF01362370
  9. Annals of Math v.128 The image of a derivation is contained in the radical M.P. Thomas https://doi.org/10.2307/1971432
  10. Glasnik Mathematicki v.26 no.46 A result concerning derivations in noncommutative Banach algebras J. Vukman
  11. Proc. Amer. Math. Soc. v.116 no.4 On derivations in prime rings and Banach algebras https://doi.org/10.2307/2159463

Cited by

  1. Generalized derivations on Lie ideals in prime rings vol.65, pp.1, 2015, https://doi.org/10.1007/s10587-015-0167-4
  2. JORDAN DERIVATIONS ON A LIE IDEAL OF A SEMIPRIME RING AND THEIR APPLICATIONS IN BANACH ALGEBRAS vol.23, pp.4, 2016, https://doi.org/10.7468/jksmeb.2016.23.4.347
  3. JORDAN DERIVATIONS ON PRIME RINGS AND THEIR APPLICATIONS IN BANACH ALGEBRAS, I vol.28, pp.3, 2013, https://doi.org/10.4134/CKMS.2013.28.3.535
  4. Engel conditions of generalized derivations on Lie ideals and left sided ideals in prime rings and Banach Algebras vol.27, pp.7-8, 2016, https://doi.org/10.1007/s13370-016-0418-z
  5. An identity with generalized derivations on lie ideals, right ideals and Banach algebras vol.62, pp.2, 2012, https://doi.org/10.1007/s10587-012-0039-0
  6. JORDAN DERIVATIONS ON PRIME RINGS AND THEIR APPLICATIONS IN BANACH ALGEBRAS, II vol.27, pp.1, 2014, https://doi.org/10.14403/jcms.2014.27.1.65