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Noetherian Domains Inside a Homomorphic Image of a Completion

✍ Scribed by William Heinzer; Christel Rotthaus; Sylvia Wiegand

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
125 KB
Volume
215
Category
Article
ISSN
0021-8693

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✦ Synopsis

Over the past 60 years, important examples of Noetherian domains have been constructed using power series, homomorphic images, and intersections. In these constructions it is often crucial that the resulting domain is computable as a directed union. In this article we analyse this construction and show that the Noetherian property for the associated directed union is equivalent to a flatness condition. Let R be a Notherian integral domain with fraction field L. Let x be a U Ε½ .

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