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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Faithful Noetherian modules


Author: Edward Formanek
Journal: Proc. Amer. Math. Soc. 41 (1973), 381-383
MSC: Primary 13E05
MathSciNet review: 0379477
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Abstract: The Eakin-Nagata theorem says that if $ T$ is a commutative Noetherian ring which is finitely generated as a module over a subring $ R$, then $ R$ is also Noetherian. This paper proves a generalization of this result. However, the main interest is that the proof is very elementary and uses little more than the definition of ``Noetherian".


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DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0379477-X
Keywords: Eakin-Nagata theorem, ascending chain condition
Article copyright: © Copyright 1973 American Mathematical Society