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Transactions of the American Mathematical Society

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A non-Noetherian factorial ring


Author: John David
Journal: Trans. Amer. Math. Soc. 169 (1972), 495-502
MSC: Primary 13H99
DOI: https://doi.org/10.1090/S0002-9947-1972-0308114-9
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.


References [Enhancements On Off] (What's this?)

  • [1] M. Nagata, Local rings, Interscience, New York, 1962. MR 27 #5790. MR 0155856 (27:5790)
  • [2] P. Samuel, Classes de diviseurs et dérivées logarithmiques, Topology 3 (1964), suppl. 1, 81-96. MR 29 #3490. MR 0166213 (29:3490)
  • [3] -, Lectures on unique factorization domains, Lectures in Math., no. 30, Tata Institute of Fundamental Research, Bombay, 1964. MR 35 #5428. MR 0214579 (35:5428)

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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

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