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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Faithful Noetherian modules
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by Edward Formanek PDF
Proc. Amer. Math. Soc. 41 (1973), 381-383 Request permission

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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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 41 (1973), 381-383
  • MSC: Primary 13E05
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0379477-X
  • MathSciNet review: 0379477