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Remarks on a Theorem of Bourbaki

Published online by Cambridge University Press:  22 January 2016

M. Auslander
M. Auslander*
Affiliation:
Brandeis University
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Bourbaki has established the following theorem which we state without proof as

THEOREM A ([3, Theorem 6, §4]). Let R be a noetherian integrally closed domain and M a finitely generated torsion free R-module. Then there exists a free submodule F of M such that M/F is isomorphic to an ideal in R.

It is our purpose in this note to present a few consequences of this theorem. Before giving these results we briefly review some terminology and known results.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 1 , February 1966 , pp. 361 - 369
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Auslander, M. and Goldman, O., Maximal orders, Trans. Amer. Math. Soc. 97 (1960), 1–24.Google Scholar
[2] Bass, H., On the ubiquity of Gorenstein rings, Math. Zeitschr. 82 (1963), 8–28.CrossRefGoogle Scholar
[3] Bourbaki, N., Elements de Mathematique, Algebre Commutative, Chapitre 7, Hermann, Paris.Google Scholar