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On a theorem of Posner

Published online by Cambridge University Press:  24 October 2008

Ram Awtar
Ram Awtar
Affiliation:
Department of Mathematics, Aligarh Muslim University, Aligarh (U.P.)India
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Extract

Posner (1) proved the following result:

Theorem. Let R be a prime ring and d a derivation of R such that, for all a∈R, ad(a)–d(a) a∈Z (centre of R). Then, if d is not a zero derivation, R is commutative.

The purpose of this note is to give a short proof of this theorem. We state the following known result ((1), Lemma 1).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 1 , January 1973 , pp. 25 - 27
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

(1)Posner, E. C.Derivations in Prime Rings. Proc. Amer. Math. Soc. 8 (1957), 1093–1100.CrossRefGoogle Scholar