Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-05T01:38:30.162Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

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