A local characterization of Noetherian and Dedekind rings
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- by Yves Lequain PDF
- Proc. Amer. Math. Soc. 94 (1985), 369-370 Request permission
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.References
- I. S. Cohen, Commutative rings with restricted minimum condition, Duke Math. J. 17 (1950), 27–42. MR 33276
- Jack Ohm and David E. Rush, The finiteness of $I$ when $\textit {R}[\textit {X}]/\textit {I}$ is flat, Trans. Amer. Math. Soc. 171 (1972), 377–408. MR 306176, DOI 10.1090/S0002-9947-1972-0306176-6
Additional Information
- © Copyright 1985 American Mathematical Society
- 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