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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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  • 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
  • Pierre Samuel, Classes de diviseurs et dérivées logarithmiques, Topology 3 (1964), no. suppl, suppl. 1, 81–96 (French). MR 166213, DOI
  • P. Samuel, Lectures on unique factorization domains, Tata Institute of Fundamental Research Lectures on Mathematics, No. 30, Tata Institute of Fundamental Research, Bombay, 1964. Notes by M. Pavman Murthy. MR 0214579

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Keywords: Factorial, Krull dimension, Noetherian, derivation, integral closure
Article copyright: © Copyright 1972 American Mathematical Society