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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A non-Noetherian factorial ring


Author: John David
Journal: Trans. Amer. Math. Soc. 169 (1972), 495-502
MSC: Primary 13H99
MathSciNet review: 0308114
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Abstract: This paper supplies a counterexample to the conjecture that factorial implies Noetherian in finite Krull dimension. The example is the integral closure of a three-dimensional Noetherian ring, and is the union of Noetherian domains, which are proven to be factorial by means of derivation techniques.


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  • [1] Masayoshi Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers a division of John Wiley & Sons New York-London, 1962. MR 0155856
  • [2] Pierre Samuel, Classes de diviseurs et dérivées logarithmiques, Topology 3 (1964), no. suppl. 1, 81–96 (French). MR 0166213
  • [3] P. Samuel, Lectures on unique factorization domains, Notes by M. Pavman Murthy. Tata Institute of Fundamental Research Lectures on Mathematics, No. 30, Tata Institute of Fundamental Research, Bombay, 1964. MR 0214579

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0308114-9
Keywords: Factorial, Krull dimension, Noetherian, derivation, integral closure
Article copyright: © Copyright 1972 American Mathematical Society