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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Jordan derivations on semiprime rings


Author: M. Brešar
Journal: Proc. Amer. Math. Soc. 104 (1988), 1003-1006
MSC: Primary 16A12; Secondary 16A72, 46H99
DOI: https://doi.org/10.1090/S0002-9939-1988-0929422-1
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].


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DOI: https://doi.org/10.1090/S0002-9939-1988-0929422-1
Keywords: Prime ring, semiprime ring, semisimple Banach algebra, derivation, Jordan derivation
Article copyright: © Copyright 1988 American Mathematical Society