Noetherian domains with many more elements than height-one primes

Author:
D. D. Anderson

Journal:
Proc. Amer. Math. Soc. **123** (1995), 2971-2974

MSC:
Primary 13F05; Secondary 13F07

DOI:
https://doi.org/10.1090/S0002-9939-1995-1264799-5

MathSciNet review:
1264799

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Abstract: Extending previous results of L. Claborn and H.W. Lenstra, Jr., we show that if *D* is a Krull domain with a set of height-one primes that satisfies either (1) *D* contains a subset *k* with and for is a unit, or (2) , then *D* is a Euclidean domain. We also show that any Noetherian ring satisfying (1) or Noetherian domain satisfying (2) has Krull dimension at most one.

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DOI:
https://doi.org/10.1090/S0002-9939-1995-1264799-5

Article copyright:
© Copyright 1995
American Mathematical Society