Pure ideals in commutative reduced Gelfand rings with unity
type: Item
instance of: scholarly article
title: Pure ideals in commutative reduced Gelfand rings with unity
zbMATH Open document ID: 0667.13001
DOI: 10.1007/BF01277063
published in: Archiv der Mathematik
publication date: 1989-01-01T00:00:00Z
review text: In this paper, pure ideals in the class of all commutative reduced Gelfand rings with unity are classified. Then as an application, we prove that any pure ideal in the ring C(X) of all continuous real valued functions over a completely regular Hausdorff space has the form \(\cap_{x\in K}0_ x \), where K is a closed subset of the Stone- Čech compactification \(\beta\) X of X.
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 54C40
Mathematics Subject Classification ID: 13C05
zbMATH DE Number: 4091624
zbMATH Keywords: ring of continuous real valued functions
zbMATH Keywords: reduced Gelfand rings
zbMATH Keywords: pure ideal
author: H. Al-Ezeh
MaRDI profile type: Publication
cites work: On some properties of polynomial rings
cites work: Algebra in a localic topos with applications to ring theory
cites work: On pm-rings
cites work: Q4092470
full work available at URL: https://doi.org/10.1007/bf01277063
OpenAlex ID: W1986264951
description: scientific article; zbMATH DE number 4091624