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Commutators in associative rings

Published online by Cambridge University Press:  24 October 2008

M. P. Drazin  and
K. W. Gruenberg
M. P. Drazin
Affiliation:
Trinity CollegeCambridge
K. W. Gruenberg
Affiliation:
Trinity CollegeCambridge
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Extract

Let R be an arbitrary associative ring, and X a set of generators of R. The elements of X generate a Lie ring, [X], say, with respect to the addition and subtraction in R, and the multiplication [a, b] = ab − ba. In this note we shall be concerned with the following question: if [X] is given to be nilpotent as a Lie ring, what does this imply about R?

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 4 , October 1953 , pp. 590 - 594
Copyright
Copyright © Cambridge Philosophical Society 1953

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References

REFERENCES

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