Approximating discrete valuation rings by regular local rings

Let k be a field of characteristic zero and let (V,\mathbf{n}) be a discrete rank-one valuation domain containing k with V/\mathbf{n}= k. Assume that the fraction field L of V has finite transcendence degree s over k. For every positive integer d \le s, we prove that V can be realized as a directed...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2001-01, Vol.129 (1), p.37-43
Main Authors: Heinzer, William, Rotthaus, Christel, Wiegand, Sylvia
Format: Article
Language:English
Subjects:
Algebra
Dilatation
Factorization
Fractions
Integers
Labor union representation
Mathematical rings
Mathematical theorems
Polynomials
Online Access:Get full text
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Summary:Let k be a field of characteristic zero and let (V,\mathbf{n}) be a discrete rank-one valuation domain containing k with V/\mathbf{n}= k. Assume that the fraction field L of V has finite transcendence degree s over k. For every positive integer d \le s, we prove that V can be realized as a directed union of regular local k-subalgebras of V of dimension d.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-00-05492-7