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A new characterization of Dedekind domains

Authors: E. W. Johnson and J. P. Lediaev
Journal: Proc. Amer. Math. Soc. 28 (1971), 63-64
MSC: Primary 13.15
MathSciNet review: 0271084
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Abstract: In this note it is shown that a Noetherian ring $ R$ is a Dedekind domain if every maximal ideal $ M$ of $ R$ satisfies the cancellation law: if $ A$ and $ B$ are nonzero ideals of $ R$ and $ MA = MB$, then $ A = B$.

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  • [1] R. W. Gilmer, Multiplicative ideal theory, Queen's Papers in Pure and Appl. Math., no. 12, Queen's University, Kingston, Ont., 1968. MR 37 #5198. MR 0229624 (37:5198)
  • [2] P. Samuel, Algèbre locale, Mèm. Sci. Math., no. 123, Gauthier-Villars, Paris, 1953. MR 14, 1012. MR 0054995 (14:1012c)
  • [3] O. Zariski and P. Samuel, Commutative algebra. Vol. 2, University Series in Higher Math., Van Nostrand, Princeton, N. J., 1960. MR 22 #11006. MR 0120249 (22:11006)

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Keywords: Dedekind domain, cancellation law
Article copyright: © Copyright 1971 American Mathematical Society

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