Completions of local rings with an isolated singularity
type: Item
instance of: scholarly article
title: Completions of local rings with an isolated singularity
zbMATH Open document ID: 0798.13009
author: Raymond C. Heitmann
published in: Journal of Algebra
publication date: 1994-04-19T00:00:00Z
review text: Let \(T\) be a complete local ring and let \(p\) be the characteristic of its residue field. The problem here is the existence of a local ring \(R\) with an isolated singularity, such that \(T\) is the completion of \(R\). The author shows that such a ring \(R\) exists if and only if for all non- maximal primes \(P \subset T\), the image of \(p\) in \(T_ P\) is either 0 or regular. This condition is easily shown to be necessary. The existence of \(R\), when the condition holds, is proved constructively starting with the prime subring \(R_ 0\) of \(T\) and extending carefully \(R_ 0\) to a ring \(R\) with \(\widehat R = T\).
Mathematics Subject Classification ID: 13J10
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13B35
zbMATH DE Number: 554220
zbMATH Keywords: complete local ring
zbMATH Keywords: isolated singularity
zbMATH Keywords: completion
reviewed by: Luca Chiantini
MaRDI profile type: Publication
full work available at URL: jabr.1994.1031
OpenAlex ID: W2084813762
DOI: 10.1006/JABR.1994.1031
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description: scientific article; zbMATH DE number 554220