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On certain subrings of prime rings with derivations

Part of: Rings and algebras with additional structure Radicals and radical properties of rings

Published online by Cambridge University Press:  09 April 2009

M. Brešar  and
J. Vukman
M. Brešar
Affiliation:
University of MariborPF, Koroška160, 62000 Maribor Slovenia
J. Vukman
Affiliation:
University of MariborPF, Koroška160, 62000 Maribor Slovenia
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Abstract

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Let D be a nonzero derivation of a noncommutative prime ring R, and let U be the subring of R generated by all [D(x), x], x ∞ R. A classical theorem of Posner asserts that U is not contained in the center of R. Under the additional assumption that the characteristic of R is not 2, we prove a more general result stating that U contains a nonzero left ideal of R as well as a nonzero right ideal of R.

Keywords

Derivationprime ringideal.

MSC classification

Secondary: 16W25: Derivations, actions of Lie algebras 16N60: Prime and semiprime rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 54 , Issue 1 , February 1993 , pp. 133 - 141
Copyright
Copyright © Australian Mathematical Society 1993

References

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