Jordan derivations on semiprime rings
HTML articles powered by AMS MathViewer
- by M. Brešar PDF
- Proc. Amer. Math. Soc. 104 (1988), 1003-1006 Request permission
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
- M. Brešar and J. Vukman, Jordan derivations on prime rings, Bull. Austral. Math. Soc. 37 (1988), no. 3, 321–322. MR 943433, DOI 10.1017/S0004972700026927
- I. N. Herstein, Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104–1110. MR 95864, DOI 10.1090/S0002-9939-1957-0095864-2
- I. N. Herstein, Topics in ring theory, University of Chicago Press, Chicago, Ill.-London, 1969. MR 0271135
- B. E. Johnson and A. M. Sinclair, Continuity of derivations and a problem of Kaplansky, Amer. J. Math. 90 (1968), 1067–1073. MR 239419, DOI 10.2307/2373290
- A. M. Sinclair, Jordan homomorphisms and derivations on semisimple Banach algebras, Proc. Amer. Math. Soc. 24 (1970), 209–214. MR 250069, DOI 10.1090/S0002-9939-1970-0250069-3
Additional Information
- © Copyright 1988 American Mathematical Society
- 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