Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


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
MathSciNet review: 1264799
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $ \vert k\vert > \vert{X^{(1)}}\vert$ and for $ \mu \ne \lambda \in k,\mu - \lambda $ is a unit, or (2) $ \vert D\vert > \vert{X^{(1)}}{\vert^{{\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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13F05, 13F07

Retrieve articles in all journals with MSC: 13F05, 13F07

Additional Information

PII: S 0002-9939(1995)1264799-5
Article copyright: © Copyright 1995 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia