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Approximating discrete valuation rings by regular local rings. (English) Zbl 0962.13017

Let \(R\) be a local ring and let \(V\) be a valuation domain that dominates \(R\). The classical methods give a representation of \(V\) as a directed union of regular local rings all having dimension equal to the dimension of \(R\) [cf. S. Abhyankar, Am. J. Math. 78, 321-348 (1956; Zbl 0074.26301)]. In this paper, using Henselization and a technique developed in their earlier works, the authors show that certain rank-one discrete valuation rings can be represented as a directed union of regular local domains of dimension \(d\) for every positive integer \(d\) less than or equal to the dimension of \(R\).

MSC:

13F30 Valuation rings
13H05 Regular local rings
13E05 Commutative Noetherian rings and modules
13G05 Integral domains
13J05 Power series rings
13J15 Henselian rings

Citations:

Zbl 0074.26301
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Full Text: DOI

References:

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