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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

(1)Drazin, M. P.Some generalizations of matrix commutativity. Proc. Land. math. Soc. (3), 1 (1951), 222–31.CrossRefGoogle Scholar
(2)Jacobson, N.Rational methods in the theory of Lie algebras. Ann. Math., Princeton (2), 36 (1935), 875–81.CrossRefGoogle Scholar
(3)Jennings, S. A.Central chains of ideals in an associative ring. Duke math. J. 9 (1942), 341–55.Google Scholar
(4)Jennings, S. A.On rings whose associated Lie rings are nilpotent. Bull. Amer. math. Soc. 53 (1947), 593–7.CrossRefGoogle Scholar