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Some examples of modules over Noetherian rings

Published online by Cambridge University Press:  18 May 2009

I. M. Musson
I. M. Musson
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, CanadaT6G 2G1.
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The purpose of this note is to prove the following result.

Theorem 1. Let n be an integer greater than zero. There exists a prime Noetherian ring R of Krull dimension n + 1 and a finitely generated essential extension W of a simple R-module V suchthat

(i) W has Krull dimension n, and

(ii) W/V is n-critical and cannot be embedded in any of its proper submodules.

We refer the reader to [6] for the definition and properties of Krull dimension.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 23 , Issue 1 , January 1982 , pp. 9 - 13
Copyright
Copyright © Glasgow Mathematical Journal Trust 1982

References

REFERENCES

1.Bohro, W., Gabriel, P. and Rentschler, R., Primideale in Einhüllenden auflösbarer Lie-Algebren Lecture Notes in Mathematics No. 357, (Springer-Verlag, 1973).Google Scholar
2.Chatters, A. W. and Hajarnavis, C. R., Kings with chain conditions (Pitman, 1980).Google Scholar
3.Dixmier, J., Enveloping algebras (North Holland, 1977).Google Scholar
4.Goldie, A. W., Properties of the idealiser, in Ring theory, Ed. Gordon, R. (Academic Press, 1972).Google Scholar
5.Goodearl, K. R., Incompressible critical modules, Comm. Algebra, 8 (1980), 1845–1852.CrossRefGoogle Scholar
6.Gordon, R. and Robson, J. C., Krull dimension, Memoirs Amer. Math. Soc. 133 (1973).Google Scholar
7.Jategaonkar, A. V., Jacobson's conjecture and modules over fully bounded Noetherian rings, J. Algebra 30 (1974), 103–121.CrossRefGoogle Scholar
8.Musson, I. M., Injective modules for group rings of polycyclic groups II, Quart. J. Math. Oxford (2), 31 (1980), 449–466.CrossRefGoogle Scholar