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Localization in enveloping algebras

Published online by Cambridge University Press:  24 October 2008

A. I. Lichtman
A. I. Lichtman
Affiliation:
Ben Gurion University of the Negev, Beer-Sheva, Israel
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Extract

Let L be a finite-dimensional Lie algebra and U(L) its universal envelope. It is known that U(L) is a Noetherian domain (see (5), theorem v. 3·4) and therefore U(L) has a field of fractions. (Throughout the paper we use the term ‘field’ in the sense of skew field.) We prove in this article the following theorem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 3 , May 1983 , pp. 467 - 475
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

REFERENCES

(1)Cohn, P. M.Free rings and their relations (Academic Press, N.Y. 1971).Google Scholar
(2)Cohn, P. M.Skew field constructions (Cambridge University Press, 1977).Google Scholar
(3)Dixmier, J.Algèbres enveloppantes (Gauthier-Villars, Paris, 1974).Google Scholar
(4)Jacobson, N.Theory of rings. (Amer. Math. Soc., Providence, 1943).CrossRefGoogle Scholar
(5)Jacobson, N.Lie algebras (Wiley, New York and London, 1962).Google Scholar
(6)Lenagan, T. H.Gelfand-Kirillov dimension in enveloping algebras. Quart. J. Math. Oxford (2) 32 (1981), 69–80.CrossRefGoogle Scholar
(7)McConnell, J. C.The intersection theorem for a class of non commutative rings. Proc. London Math. Soc. (3), 17 (1967), 487–498.CrossRefGoogle Scholar
(8)McConnell, J. C.Localization in enveloping rings. J. London Math. Soc. 43 (1968), 421–428.CrossRefGoogle Scholar
(9)McConnell, J. C.Localization in enveloping rings: Erratum and Addendum. J. London Math. Soc. (2), 3 (1971), 405–410.Google Scholar
(10)Passman, D. S.The algebraic structure of group rings (Wiley, New York, 1977).Google Scholar
(11)Passman, D. S.Universal fields of fractions for polycyclic group algebras. Glasgow Math. Journal 23 (1982), 103–113.CrossRefGoogle Scholar
(12)Roseblade, J. E.Applications of the Artin-Rees lemma to group rings. Symp. Math. 17 (1976).Google Scholar
(13)Smith, P. F.Localization and AR property. Proc. London Math. Soc. 22 (1971), 39–69.CrossRefGoogle Scholar