Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Discrete valuation overrings
of Noetherian domains


Authors: Paul-Jean Cahen, Evan G. Houston and Thomas G. Lucas
Journal: Proc. Amer. Math. Soc. 124 (1996), 1719-1721
MSC (1991): Primary 13E05, 13A18; Secondary 13G05, 13A15
MathSciNet review: 1317033
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that, given a chain $0=P_0\subset P_1\subset \dotsb \subset P_n$ of prime ideals in a Noetherian domain $R$, there exist a finitely generated overring $T$ of $R$ and a saturated chain of primes in $T$ contracting term by term to the given chain. We further show that there is a discrete rank $n$ valuation overring of $R$ whose primes contract to those of the given chain.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 13E05, 13A18, 13G05, 13A15

Retrieve articles in all journals with MSC (1991): 13E05, 13A18, 13G05, 13A15


Additional Information

Paul-Jean Cahen
Affiliation: (P.-J. Cahen) Service de Mathématiques 322, Faculté des Sciences de Saint-Jérôme, 13397 Marseille cedex 20, CNRS URA 225, France
Email: cahen@vmesal2.u-3mrs.fr

Evan G. Houston
Affiliation: (E. G. Houston and T. G. Lucas) Department of Mathematics, University of North Carolina at Charlotte, Charlotte, North Carolina 28223
Email: fma00egh@unccvm.uncc.edu

Thomas G. Lucas
Email: tglucas@unccsun.uncc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03260-1
PII: S 0002-9939(96)03260-1
Received by editor(s): October 24, 1994
Received by editor(s) in revised form: December 16, 1994
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1996 American Mathematical Society