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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A new characterization of Dedekind domains
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by E. W. Johnson and J. P. Lediaev PDF
Proc. Amer. Math. Soc. 28 (1971), 63-64 Request permission

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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Additional 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