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Primary decomposition in enveloping algebras

Published online by Cambridge University Press:  20 January 2009

K. A. Brown  and
T. H. Lenagan
K. A. Brown
Affiliation:
University of Glasgow
T. H. Lenagan
Affiliation:
University of Edinburgh
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Recently, the first author and, independently, A. V. Jategaonkar have shown that every factor ring of U(g), the universal enveloping algebra of a finite dimensional complex Lie algebra, has a primary decomposition if g is solvable and almost algebraic. On the other hand, a suitable factor ring of U(SL(2, ℂ) fails to have a primary decomposition (1).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 24 , Issue 2 , June 1981 , pp. 83 - 85
Copyright
Copyright © Edinburgh Mathematical Society 1981

References

REFERENCES

(1)Brown, K. A., Module extensions over Noetherian rings, J. of Algebra, to appear.Google Scholar
(2)Dixmier, J., Algèbres Enveloppantes (Gauthier-Villars, Paris, 1974).Google Scholar
(3)Ginn, S. M. and Moss, P. B., Finitely embedded modules over Noetherian rings, Bull. Amer. Math. Soc. 81 (1975), 709–710.CrossRefGoogle Scholar
(4)Gordon, R., Primary decomposition in right Noetherian rings, Comm. in Algebra 2 (1974), 491–524.CrossRefGoogle Scholar
(5)Krause, G., Lenagan, T. H. and Stafford, J. T., Ideal Invariance and Artinian Quotient rings, J. of Algebra 55 (1978), 145–154.CrossRefGoogle Scholar
(6)McConnell, J. C., Localisation in enveloping rings, J. London Math. Soc. 43 (1968), 421–428.CrossRefGoogle Scholar