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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

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