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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A codimension theorem for pseudo-Noetherian rings


Author: Kenneth McDowell
Journal: Trans. Amer. Math. Soc. 214 (1975), 179-185
MSC: Primary 13C15
MathSciNet review: 0382252
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Abstract: M. Auslander and M. Bridger have shown that the depth of a Noetherian local ring is the sum of the Gorenstein dimension and the depth of any given nonzero finitely generated module of finite Gorenstein dimension. In this paper it is demonstrated that this result remains true when suitably interpreted for the class of coherent rings herein entitled pseudo-Noetherian rings. This class contains, among others, all Noetherian rings and valuation domains as well as non-Noetherian local rings of infinite depth.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0382252-X
PII: S 0002-9947(1975)0382252-X
Keywords: Coherent ring, projective dimension, Gorenstein dimension, depth of a module
Article copyright: © Copyright 1975 American Mathematical Society