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
DOI:
https://doi.org/10.1090/S0002-9939-96-03260-1
MathSciNet review:
1317033
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We show that, given a chain of prime ideals in a Noetherian domain
, there exist a finitely generated overring
of
and a saturated chain of primes in
contracting term by term to the given chain. We further show that there is a discrete rank
valuation overring of
whose primes contract to those of the given chain.
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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:
https://doi.org/10.1090/S0002-9939-96-03260-1
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