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Derivations on semiprime rings

Published online by Cambridge University Press:  17 April 2009

Joso Vukman
Affiliation:
Department of MathematicsUniversity of MariborPF, Koroška 16062000 MariborSlovenia
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Abstract

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The main result: Let R be a 2-torson free semiprime ring and let D: RR be a derivation. Suppose that [[D(x), x], x] = 0 holds for all xR. In this case [D(x), x] = 0 holds for all xR.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Brešar, M. and Vukman, J., ‘Orthogonal derivation and an extension of a theorem of Posner’, Rad Mat. 5 (1989), 237246.Google Scholar
[2]Brešar, M., ‘On a generalization of the notion of centralising mappings’, Proc. Amer. Math. Soc. 114 (1992), 641649.CrossRefGoogle Scholar
[3]Brešar, M., ‘Commuting traces of biaditive mappings, commutativity-preserving mappings and Lie mappings’, Trans. Amer. Math. Soc. 335 (1993), 525546.CrossRefGoogle Scholar
[4]Brešar, M., ‘Centralizing mappings and derivations in prime rings’, J. Algebra 156 (1993), 385394.CrossRefGoogle Scholar
[5]Lanski, C., ‘An Engel condition with derivations’, Proc. Amer. Math. Soc. 118 (1993), 731734.CrossRefGoogle Scholar
[6]Posner, E.C., ‘Derivations in prime rings’, Proc. Amer. Math. Soc. 8 (1957), 10931100.CrossRefGoogle Scholar
[7]Vukman, J., ‘Commuting and centralizing mappings in prime rings’, Proc. Amer. Math. Soc. 109 (1990), 4752.CrossRefGoogle Scholar