Relations between localizations and \(I\)-adic completions in commutative domains
type: Item
instance of: scholarly article
title: Relations between localizations and \(I\)-adic completions in commutative domains
zbMATH Open document ID: 0927.13014
author: P. Zanardo
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1998-10-27T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108475
review text: The paper starts with an example of a domain \(R\), complete in its \({\mathfrak P}\)-adic topology, where \({\mathfrak P}\) is not maximal and the \({\mathfrak P}\)-adic topology is not equivalent to the natural one, but \(R_{\mathfrak P}\) is complete in the \({\mathfrak P}_{\mathfrak P}\)-adic topology. Then, the author states conditions for a commutative domain \(R\), endowed with a Hausdorff \({\mathfrak I}\)-adic topology, to give rise to a local ring \(R_{\mathfrak P}\), \({\mathfrak P}\supset {\mathfrak I}\), not complete with respect to its \({\mathfrak I}_{\mathfrak P}\)-adic topology.
Mathematics Subject Classification ID: 13B35
Mathematics Subject Classification ID: 13B30
Mathematics Subject Classification ID: 13J10
zbMATH DE Number: 1183141
zbMATH Keywords: localizations
zbMATH Keywords: completions
zbMATH Keywords: adic topology
reviewed by: Carla Massaza
MaRDI profile type: Publication
cites work: The Krull intersection theorem
cites work: Q5563439
cites work: Differentialrechnung in der analytischen Geometrie
cites work: Q5605293
cites work: Primary decomposition of divisorial ideals in Mori domains
cites work: Q4052239
cites work: Modules over domains large in a complete discrete valuation ring
cites work: Q5735274
cites work: Commutative domains large in their \({\mathfrak M}\)-adic completions
description: scientific article; zbMATH DE number 1183141