On an Euler product ring
type: Item
instance of: scholarly article
title: On an Euler product ring
zbMATH Open document ID: 0599.12010
author: Nobushige Kurokawa
published in: Proceedings of the Japan Academy. Series A
publication date: 1985-01-01T00:00:00Z
review text: The author studies the completion \(\hat A=\prod_{{\mathfrak p}}A_{{\mathfrak p}}\) of the ring A of integers in some finite number field F. Using results from nonstandard number theory he proves that the space \(M(\hat A)\) of maximal ideals is Hausdorff compact and that the space \(\Omega(\hat A)\) of Kähler differentials does not vanish. Finally he mentions results on the analytic behaviour of special zeta functions being the product of infinitely, but not cofinitely many local Euler factors.
Mathematics Subject Classification ID: 11R42
Mathematics Subject Classification ID: 13J10
Mathematics Subject Classification ID: 11S85
Mathematics Subject Classification ID: 12L15
zbMATH DE Number: 3966225
zbMATH Keywords: rings of integers
zbMATH Keywords: Euler products
zbMATH Keywords: nonstandard arithmetic
zbMATH Keywords: completion
zbMATH Keywords: nonstandard number theory
zbMATH Keywords: maximal ideals
zbMATH Keywords: Kähler differentials
zbMATH Keywords: zeta functions
reviewed by: Norbert Klingen
MaRDI profile type: Publication
full work available at URL: pjaa.61.262
OpenAlex ID: W2047150463
cites work: Q4085720
cites work: Zur Idealstruktur in Nichtstandardmodellen von Dedekindringen.
cites work: Ultraproducts in the theory of models
cites work: On some Euler products. II
cites work: Compactification of groups and rings and nonstandard analysis
DOI: 10.3792/PJAA.61.262
description: scientific article; zbMATH DE number 3966225