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Proceedings of the American Mathematical Society

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



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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  • Robert W. Gilmer, Multiplicative ideal theory, Queen’s Papers in Pure and Applied Mathematics, No. 12, Queen’s University, Kingston, Ont., 1968. MR 0229624
  • Pierre Samuel, Algèbre locale, Mémor. Sci. Math., no. 123, Gauthier-Villars, Paris, 1953 (French). MR 0054995
  • Oscar Zariski and Pierre Samuel, Commutative algebra. Vol. II, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-London-New York, 1960. MR 0120249

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