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Proceedings of the American Mathematical Society

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

 

 

A local characterization of Noetherian and Dedekind rings


Author: Yves Lequain
Journal: Proc. Amer. Math. Soc. 94 (1985), 369-370
MSC: Primary 13E05; Secondary 13F05
DOI: https://doi.org/10.1090/S0002-9939-1985-0787874-1
MathSciNet review: 787874
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Abstract: Let $ R$ be a ring and $ M$ a maximal ideal of $ R$. Then $ R$ is Noetherian if and only if every ideal contained in $ M$ is finitely generated; $ R$ is Dedekind if and only if every nonzero ideal contained in $ M$ is invertible.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0787874-1
Article copyright: © Copyright 1985 American Mathematical Society