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Transactions of the American Mathematical Society

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

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A non-Noetherian factorial ring
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by John David PDF
Trans. Amer. Math. Soc. 169 (1972), 495-502 Request permission

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
  • Masayoshi Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers (a division of John Wiley & Sons, Inc.), 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 10.1016/0040-9383(64)90006-0
  • 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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Additional Information
  • © Copyright 1972 American Mathematical Society
  • 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