Discrete rings
type: Item
instance of: scholarly article
title: Discrete rings
zbMATH Open document ID: 0873.12006
DOI: 10.1016/0022-4049(95)00107-7
author: Niel Shell
published in: Journal of Pure and Applied Algebra
publication date: 1996-08-25T00:00:00Z
review text: An absolute value on a field \(F\) is a function \(\varphi: F\to \mathbb{R}^\geq\) which is either a Krull valuation or the restriction of (some power of) the usual absolute value of \(\mathbb{C}\) to a subfield. An absolute value defines a topology on the field \(F\), hence, by restriction, also on every subring (unitary or not). The author studies subrings that are discrete, notably for the cases that \(F\) is the completion of a function field \(K(X)\) in one variable with respect to the \((1/X)\)-adic topology, or that \(F\) is \(\mathbb{R}\) or \(\mathbb{C}\) with the usual absolute value.
reviewed by: Niels Schwartz
Mathematics Subject Classification ID: 12J10
Mathematics Subject Classification ID: 13J99
Mathematics Subject Classification ID: 12J05
zbMATH DE Number: 920035
zbMATH Keywords: discrete rings
zbMATH Keywords: topological field
zbMATH Keywords: valuation
zbMATH Keywords: normal ring
zbMATH Keywords: absolute value
MaRDI profile type: Publication
full work available at URL: 0022-4049(95)00107-7
OpenAlex ID: W4210411793
cites work: Q5723264
cites work: Maximal and Minimal Ring Topologies
cites work: Q3999309
cites work: Q4228847
cites work: Q4373435
cites work: Direct topologies from discrete rings. II
description: scientific article; zbMATH DE number 920035