Noetherian domains with many more elements than height-one primes

Anderson, D. D.

doi:10.1090/S0002-9939-1995-1264799-5

Noetherian domains with many more elements than height-one primes
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Proc. Amer. Math. Soc. 123 (1995), 2971-2974 Request permission

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 ${X^{(1)}}$ that satisfies either (1) D contains a subset k with $|k| > |{X^{(1)}}|$ and for $\mu \ne \lambda \in k,\mu - \lambda$ is a unit, or (2) $|D| > |{X^{(1)}}{|^{{\aleph _0}}}$, 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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