Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Discrete valuation overrings of Noetherian domains

Author(s): Paul-Jean Cahen; Evan G. Houston; 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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