Faithful Noetherian modules
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- by Edward Formanek
- Proc. Amer. Math. Soc. 41 (1973), 381-383
- DOI: https://doi.org/10.1090/S0002-9939-1973-0379477-X
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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".References
- Jan-Erik Björk, Noetherian and Artinian chain conditions of associative rings, Arch. Math. (Basel) 24 (1973), 366–378. MR 344286, DOI 10.1007/BF01228225
- Paul M. Eakin Jr., The converse to a well known theorem on Noetherian rings, Math. Ann. 177 (1968), 278–282. MR 225767, DOI 10.1007/BF01350720
- David Eisenbud, Subrings of Artinian and Noetherian rings, Math. Ann. 185 (1970), 247–249. MR 262275, DOI 10.1007/BF01350264
- Edward Formanek and Arun Vinayak Jategaonkar, Subrings of Noetherian rings, Proc. Amer. Math. Soc. 46 (1974), 181–186. MR 414625, DOI 10.1090/S0002-9939-1974-0414625-5
- Irving Kaplansky, Commutative rings, Allyn and Bacon, Inc., Boston, Mass., 1970. MR 0254021
- Daniel Mollier, Descente de la propriété noethérienne, Bull. Sci. Math. (2) 94 (1970), 25–31 (French). MR 269638
- Masayoshi Nagata, A type of subrings of a noetherian ring, J. Math. Kyoto Univ. 8 (1968), 465–467. MR 236162, DOI 10.1215/kjm/1250524062
Bibliographic 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