Discrete valuation overrings of Noetherian domains
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- by Paul-Jean Cahen, Evan G. Houston and Thomas G. Lucas PDF
- Proc. Amer. Math. Soc. 124 (1996), 1719-1721 Request permission
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
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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
- Received by editor(s): October 24, 1994
- Received by editor(s) in revised form: December 16, 1994
- Communicated by: Wolmer V. Vasconcelos
- © Copyright 1996 American Mathematical Society
- 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