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On the nilpotence of nil ideals

Published online by Cambridge University Press:  24 October 2008

R. E. Macrae
R. E. Macrae
Affiliation:
The University, Sheffield*
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Extract

One of the classical results of ring theory is due to Levitzki ((3), p. 199) and asserts the equivalence of the notions of nil and nilpotent one-sided ideals in a ring satisfying the ascending chain condition on left ideals. Recent, distinctive proofs of this result have been given by Goldie (1) and Herstein (2). We present below yet a fourth way of proving Levitzki's theorem.

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 3 , July 1963 , pp. 679 - 680
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCES

(1)Goldie, A. W., Semi-prime rings with maximum condition. Proc. London Math. Soc. 10 (1960), 201–220.CrossRefGoogle Scholar
(2)Herstein, I. N., A theorem of Levitzki. Proc. American Math Soc. 13 (1962), 213–214.Google Scholar
(3)Jacobson, N., The structure of rings (American Mathematical Society; Providence, R.I., 1956).CrossRefGoogle Scholar