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
MathSciNet review: 787874
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Abstract: Let be a ring and a maximal ideal of . Then is Noetherian if and only if every ideal contained in is finitely generated; is Dedekind if and only if every nonzero ideal contained in is invertible.