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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  • [1] Robert W. Gilmer, Multiplicative ideal theory, Queen’s Papers in Pure and Applied Mathematics, No. 12, Queen’s University, Kingston, Ont., 1968. MR 0229624
  • [2] Pierre Samuel, Algèbre locale, Mémor. Sci. Math., no. 123, Gauthier-Villars, Paris, 1953 (French). MR 0054995
  • [3] 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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0271084-0
Keywords: Dedekind domain, cancellation law
Article copyright: © Copyright 1971 American Mathematical Society