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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
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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.

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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

Evan G. Houston
Affiliation: (E. G. Houston and T. G. Lucas) Department of Mathematics, University of North Carolina at Charlotte, Charlotte, North Carolina 28223

Thomas G. Lucas

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