Noetherian domains with many more elements than height-one primes

D.D. Anderson

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

Back

Noetherian domains with many more elements than height-one primes

Journal article

Open access

Peer reviewed

Noetherian domains with many more elements than height-one primes

D.D. Anderson

Proceedings of the American Mathematical Society, Vol.123(10), pp.2971-2974

1995

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

Files and links (1)

url

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

Published (Version of record) Open Access

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 ε ≠ λ ϵ k, ε - λ 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. © 1995 American Mathematical Society.

Details

Title: Subtitle: Noetherian domains with many more elements than height-one primes
Creators: D.D. Anderson
Resource Type: Journal article
Publication Details: Proceedings of the American Mathematical Society, Vol.123(10), pp.2971-2974
DOI: 10.1090/S0002-9939-1995-1264799-5
ISSN: 0002-9939
Language: English
Date published: 1995
Academic Unit: Mathematics
Record Identifier: 9984230420302771

Metrics

14 Record Views