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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
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.


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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