Irreducibility in approximation couples
type: Item
instance of: scholarly article
title: Irreducibility in approximation couples
zbMATH Open document ID: 0801.12002
DOI: 10.1007/BF01876310
author: V. K. Grover
author: N. Sankaran
published in: Periodica Mathematica Hungarica
publication date: 1994-03-01T00:00:00Z
review text: For a pair \(A\subset \overline{A}\) of commutative rings such that \(A\) has a linear Hausdorff topology given by a filtration of ideals and \(A\) is dense in \(\overline{A}\), we say that the couple \((A, \overline{A})\) has the Artin approximation property if for any solution in \(\overline{A}\) of a system of polynomials over \(A\) one can find an arbitrarily close approximation in \(A\) which is again a solution. This paper will prove the following Theorem: If \(A\subset \overline{A}\) are integral domains with the approximation property and \(A\) is complete and Hilbertian then \(\overline{A}\) is Hilbertian. The proof is short and elementary.
Mathematics Subject Classification ID: 12E25
Mathematics Subject Classification ID: 14B12
zbMATH DE Number: 508814
zbMATH Keywords: Hilbertian field
zbMATH Keywords: Artin approximation
MaRDI profile type: Publication
cites work: Algebraic approximation of structures over complete local rings
cites work: Q3325851
cites work: Über Hilbertsche Körper.
cites work: Q3794293
cites work: Approximation properties for some non-Noetherian local rings
full work available at URL: https://doi.org/10.1007/bf01876310
OpenAlex ID: W1997320155
description: scientific article; zbMATH DE number 508814