Integral closures of ideals in completions of regular local domains

dc.creatorHeinzer, William
dc.creatorRotthaus, Christel
dc.creatorWiegand, Sylvia
dc.date2004-05-16
dc.date.accessioned2026-07-07T05:08:19Z
dc.date.available2026-07-07T05:08:19Z
dc.descriptionIn this paper we exhibit an example of a three-dimensional regular local domain (A, n) having a height-two prime ideal P with the property that the extension PA^ of P to the n-adic completion A^ of A is not integrally closed. We use a construction we have studied in earlier papers: For R=k[x,y,z], where k is a field of characteristic zero and x,y,z are indeterminates over k, the example A is an intersection of the localization of the power series ring k[y,z][[x]] at the maximal ideal (x,y,z) with the field k(x,y,z,f, g) where f, g are elements of (x,y,z)k[y,z][[x]] that are algebraically independent over k(x,y,z). The elements f, g are chosen in such a way that using results from our earlier papers A is Noetherian and it is possible to describe A as a nested union of rings associated to A that are localized polynomial rings over k in five variables.
dc.description9 pages
dc.identifierhttps://arxiv.org/abs/math/0405315
dc.identifierhttp://arxiv.org/abs/math/0405315
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71215
dc.subjectCommutative Algebra
dc.subject13H05
dc.titleIntegral closures of ideals in completions of regular local domains
dc.typetext

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