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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A new characterization of Dedekind domains
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by E. W. Johnson and J. P. Lediaev
Proc. Amer. Math. Soc. 28 (1971), 63-64
DOI: https://doi.org/10.1090/S0002-9939-1971-0271084-0
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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 $A = B$.
References
  • 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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Bibliographic Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 28 (1971), 63-64
  • MSC: Primary 13.15
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0271084-0
  • MathSciNet review: 0271084