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Jordan derivations on semiprime rings

Author: M. Brešar
Journal: Proc. Amer. Math. Soc. 104 (1988), 1003-1006
MSC: Primary 16A12; Secondary 16A72, 46H99
MathSciNet review: 929422
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Abstract: I. N. Herstein has proved that any Jordan derivation on a $ 2$-torsion free prime ring is a derivation. In this paper we prove that Herstein's result is true in $ 2$-torsion free semiprime rings. This result makes it possible for us to prove that any linear Jordan derivation on a semisimple Banach algebra is continuous, which gives an affirmative answer to the question posed by A. M. Sinclair in [5].

References [Enhancements On Off] (What's this?)

  • [1] M. Brešar and J. Vukman, Jordan derivations on prime rings, Bull. Austral. Math. Soc. 37 (1988), 321-322. MR 943433 (89f:16049)
  • [2] I. N. Herstein, Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104-1110. MR 0095864 (20:2362)
  • [3] -, Topics in ring theory, Univ. of Chicago Press, Chicago, London, 1969. MR 0271135 (42:6018)
  • [4] B. E. Johnson and A. M. Sinclair, Continuity of derivations and a problem of Kaplansky, Amer. J. Math. 90 (1968), 1067-1073. MR 0239419 (39:776)
  • [5] A. M. Sinclair, Jordan homomorphisms and derivations on semisimple Banach algebras, Proc. Amer. Math. Soc. 24 (1970), 209-214. MR 0250069 (40:3310)

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Keywords: Prime ring, semiprime ring, semisimple Banach algebra, derivation, Jordan derivation
Article copyright: © Copyright 1988 American Mathematical Society

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