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Products of derivations

Published online by Cambridge University Press:  20 January 2009

T. Creedon
T. Creedon
Affiliation:
Department of Mathematics, University College, Cork, Ireland
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Abstract

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We prove that if the product of two derivations on an algebra is a derivation, then the product maps the algebra into its nilradical. As a consequence we obtain a characterisation of when the product of two derivations on a semiprime algebra is a derivation. We also give a condition on two derivations on a Banach algebra which implies that their product has range contained in the Jacobson radical.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 41 , Issue 2 , June 1998 , pp. 407 - 410
Copyright
Copyright © Edinburgh Mathematical Society 1998

References

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